There probably isn't a better place to target tarpon in May than the Florida Keys. That's when the main body of fish are migrating into and through the area before heading up either side of Florida, and of all the great spots to catch them in the Keys, my favorite is around Long Key.
If you're a fly fishing guy, the two corners of the Long Key Bridge have nice white sand and points where the fish track really well. That's on the ocean side of Long Key.
If you're a bait guy, the bridge itself, with a lot of the best fishing from the center of the span to 100 yards left or right of it. Most people fish live mullet and anchor on the up-current side and let their baits go under the bridge. Crabs work well too, especially as we get a little later in May. Pilchards will work if you have a bunch and can live chum a little bit and get the fish feeding.
The majority of the fish around the bridge are hovering near the bottom, so the fish you see rolling only represent a small minority of the number of fish in the area. Sometimes they're stacked 100 fish in every stall of the bridge, and that's when a dead mullet, split-tailed and sitting on the bottom is a great bait. The fish are basically scavengers, so they'll suck a dead mullet off the boat in a second.
I'm a big fan of circle hooks and light leader for tarpon fishing in the Keys. The water is super clear most of the time, so I never go over 60 pound fluorocarbon leader and will use a 5/0 for a crab and a 6/0 to 8/0 hook for a live bait. Twenty pound spinning or conventional tackle will keep things sporty. Keep in mind that because you're fishing near the bridge, when you hook up to a fish that's 100 pounds or more, you're more than likely going to be following it through the bridge. You'll want a quick release anchor system, with a float so you can release the anchor to follow the fish, then come right back to the same spot after you land it and set up again.
A fair number of fishing guides like to target tarpon at night, and I don't know if the bite is any better, but the pressure on the fish is usually lighter. The down side is that the current will really be moving through the bridges, especially on a new or full moon, and you don't want to be racing around the bridge in the dark with a strong current if you don't know what you're doing. Also, I like to see the fish when they eat, so I fish them almost exclusively during the daytime.
The Keys get crowded during tarpon season, so be sure to give other fishermen plenty of room any time you're fishing. Extend the courtesy to them, and they'll reciprocate in spades.