What characterizes a "wet fly" rod?

I'm mostly fishing wets (soft hackle un-weighted) and usually fishing a FF755 or a FR2000 5wt. They cast and fish fine but sometimes it's a struggle pulling fish (trout) back upstream in heavier currents.

Am I asking too much of 5 weight rods? Or are they more dry fly rods and a wet fly rod would work better?

A slower more full flexing rod is well suited for throwing a more gentle open loop which can be helpful to avoid tangles when casting a pair of flies. Also, strikes on a down and across drift can be violent and because there is little slack in the line, the softer rod will act more as a shock absorber to protect the tippet. You can fish soft hackles and wets with pretty much any rod if you don't forget to compensate with rod angle and careful line management. Landing a large downstream fish is a challenge no matter what rod you use. I will use a heavier tippet for this type of fly fishing both to avoid breaking off on the strike and for landing downstream fish. Usually 3x or even 2x. IMO, these heavier tippets don't spook fish when they are under water.

Yes, tiptop has you covered. In the old days, a "gang" of wet flies--three, typically--was best cast with a full-flexing (almost C-shaped at max load) rod so the flies and the dropper loops didn't snarl up. The other reason is that fish will often slaughter a swung wet fly, so the rod needed to absorb that shock to minimize break offs on the strike. In between the cast and the strike, the full flex rod enabled swimming or pulsing or directing the flies by throwing a pulse of line (mending the line with a roll) to fish the fly the way the fish wanted to see it, and where the fish wanted to hammer it. Gosh, it is a fun way to fish, and absolutely, stronger tippets are all advantage. The quicker the water, the more you can go up from what you would use for a delicate dry-fly drift.

Interesting about using stronger tippet … makes perfect sense. For all practical purposes are wet flies and soft hackles fished with the same techniques? Swinging them across and down and pulsing?

Great discussion above... for me, super slow and long probably means split cane. I have handled so many well designed longer glass rods and with slowness comes too much power for me. I would love to hear Mike McFarland and/or Larry Kenney on the difficulties, if any, of designing longer glass rods that are truly delicate and soft.

Glass is too powerful dynamically, in my hand. Just my thoughts... Wet flies, especially downstream, need to be handled with a soft action for takes and open loops and avoidance of false casts. If you run across a buddy with an old Leonard Catskill 9 footer that has an actual weight of 4 ounces, pick it up and the wiggle test will tell you it is unfishable. Don't listen - string it up with a heavier line, maybe a 5 and a long leader. Add a couple of small wets and fish it up or down... Pond or stream or river - you will have a blast...

On shrunken, high pressured, clear eastern streams, a very long leader and long downstream swings and pauses are the way to really enjoy those quiet waters and beautiful afternoons...
On second thought, I remember an early honey Lami glass rod of 8' designed for a 5 that would do well for wet flies and spider...
On third thought, the longer James Green NTS or HTS rods might be just fine...

That's the typical way to fish them. Controlling the drift speed by mending makes it more effective.

Lots of ways to fish wets though.

Dave Hughes has written the definitive book: Wet Flies 2nd Edition. He goes into the history, tying instructions and fishing techniques.

Highly recommended!

Soft hackles are a form of "wet fly," which is really just a generic term for flies fished subsurface. We think of "wet fly" relative to some traditional patterns because that is when the term was most commonly used. Lots of specialty terms for subsets of flies, dry (to be fished floating) or wet (to be fished subsurface) have come into common use since. These are ways of distinguishing fly styles more than fishing method.

Old school wet flies can be fished upstream, dead drifted, and so on. Soft hackles can as well, and "dry" for longer float period than a traditional wet fly, basically because they can be fluffed with fewer false casts. Either can be fished all those ways on one presentation if the stream form invites it.

Fiberglass is amply resilient to absorb hard strikes, especially in moderate to full flex actions, but progressive actions do it well also. Fishing a gang of wetflies is fun, but after doing it a few times and learning the presentation patterns, usually one fly is sufficient. You learn the presentation point, the fish's look point, and the strike point and get to know when a strike is coming, thus handling the strike and first run more adeptly. A few doubles with big fish also convinces you to give up the extra flies. You can land a double now and then, but the ensuing tangle and untangling and releasing the fish costs time that costs fish. The more you fish this way, the less passive swinging and wondering which fly the fish might like, and the more learned to put the one in the right place to be seen and attacked.

Often that's at the tail of a pool after a swing started far above it. When fish are feeding on floating prey, they are more likely to gently sip and settle, enabling a gradual hook set, making it more likely they stay in the pool. In attack mode on what they perceive as struggling and escaping prey (the swung "wet fly") , the takes are more aggressive, so bolt and run is more likely. Sometimes they run upstream, but if they run out of the pool, hold on. That's when you will be glad again for the heavier tippet chosen, and might consider a 6 or 7 weight glass rod the next time, especially if fishing where you can't scramble downstream to get below the fish. Afterall, when "wet fly" fishing was common the all-around rods used were for D and C lines.

A variation is when the swing stops, the line bellies tighter, and you think you are hung up on a rock. Just in case, imagine it could be a big lazy fish with a fully belly that doesn't want to move any more than it has to. It is probably a rock. Lift up anyway. Tap the rod but or strum the tight line a few times. Sometimes the "rock" moves.

What tiptop said about the rods.

I quit tying winged wets years ago, about the same week I quit tying winged dries. My belief being the wings were for the buyer rather than the fish and I wasn't selling flies. However I fish wets up, down, across, at any water depth including the surface and occasionally even dead drift one, but having understood Sawyer's induced take and Leisenring's lift to mean that fish like living, moving bait; my wet fly presentation is almost always on a taut line with some added motion.
I also don't usually "swing" flies in the traditional sense, as mentioned above the take is often after the swing is almost complete after eons of time and miles of water have been crossed, so, with me being rather short on patience and very easily bored, I most often target the spot a yard or so above the expected take and maintain the swing for a couple yards past the expected taking point. I surely miss a few fish this way but I can cover most of the actual productive water in two or three yard swings rather than casting and waiting and waiting and dozing off just when the fly arrives at the fish. When I do cast to the swing place the swing is considerably shortened by stripping and mending to give changes of direction, depth and speed to the the "swimming" fly and to keep me interested.

I used to fish a lot of "teams" of flies (or as I called them "flights") 2, 3, 5 and though I caught a lot of trout that way I quit that for the most part in the late '80s, and it never seemed to mean fewer fish at the end of the day. It did mean less time rigging and tearing down the rig. When I moved back to Mo. the "Fly only" regs called for a "single point hook" which I mistakenly thought said a "single hook" and it wasn't until years later I discovered in another part of the regs that we are allowed up to three hooks, or flies; just not allowed doubles or trebles. I've occasionally used two or three flies since, but never with any great difference in results.

I liked Dave Hughes' book, but it's rare i don't like book on fly fishing.

If I have two wets on, and they’re taking just one, I’ll usually keep both of them on until something happens to force me to re-rig. I’m always worried that taking one off the rig will alter the mechanics that assisted the success.

To begin with, in your opening post you asked whether a 5-weight is heavy enough for wet fly fishing. In my experience it should be. One important detail is to avoid keeping the rod pointed at the fly; rather, keep it at enough of an angle so that the rod tip will help absorb the shock of a take.

Regarding the tippet size, let’s say that around 6 # test should be about right. That could be 3X or even 4X, depending on the brand.

You stated, "One of the many things I learned from Dave Hughes's book is to attach the dropper to the eye of the lead fly. That really seems to work better than tag ends and such. A lot less tangle. I've never liked attaching the dropper to the bend of the hook. Yea I know everyone does it but it doesn't seem secure to me. Dave prefers to fish one fly too."

Thanks, I didn’t know that. My experience in fishing multi-fly rigs dates back to sometime in the ‘70s. My sources of information must have been either Ray Bergman’s “Trout”, or AJ McClane’s “Standard Fishing Encyclopedia”. Incidentally, my understanding of droppers is a bit traditional, described as follows.

“Dropper: A term applied in wet fly fishing, both to the strand of nylon on which a second or third fly is fished, and to those flies themselves… The knots used to form droppers on a leader are usually the Blood Knot or the Water Knot (see knots).” Source: “A Dictionary of Fly Fishing”, by C.B. McCully, published by Oxford University Press in 1993.

My rig would be based on the Ritz formula leader, simply leaving a long tag end on the blood knots that I wanted to use as droppers. Nowadays I prefer the Double or Triple Surgeon’s Knot. The tag is cut at about 6” long, so that with a fly attached it is no longer that 3” or 4”. Anything beyond that is an invitation to tangles. My point fly, at the end of the leader, is usually a streamer or a weighted nymph, with soft-hackle wets on the droppers.

The terminology has apparently been changed in recent years, just to confuse matters even more.

By the way, while I'm not a great fly caster, two things have helped my casting a lot. One is fishing with multi-fly rigs, because when my casting stroke isn't just right, I get punished with tangles. The other is fishing after dark because then it becomes necessary to rely on feeling the rod load to get the timing right.

I'll second Specs recommendation above to read Dave Hughes' book on Wet Flies. Informative for history, tying patterns, and technique. After reading his Wet Flies, I went on to buy several more of his books.