We just got back from 5 days in Key Largo. I dove lots of their wrecks, the Duane twice, Spiegel Grove 3 times, Bibb once and Benwood - a lesser wreck - twice. Nice dives, one of the days was glorious - dead calm, 80' vis.
We dive with Rainbow Reef, the only operator in the Keys, that I know, that has dive masters in the water with you. I like dive masters.
A quick story. Did one night dive with another operator, who I think are generally good. But no dive masters. My buddy for that night was taking a hyberbaric class, an active duty Navy guy - younger and more fit than my 64 yr old bod. It was his only dive during his one week class, he said he would follow me. As is the norm, there was a mild current. We eventually drifted down current maybe 100 yrds from the boat. I popped up to find the boat, took a compass reading and went back down to 25'. My buddy then popped up, I went back up with him and he said he was out of air and proceeded to abruptly surface swim back to the boat. He had 1,300psi about 2 minutes earlier - he was clearly scared that I would not lead him back to the boat underwater. So, we beat it back on a surface swim and missed about 1/2 of the dive. If a dive master had been down with us there would have been no anxiety and we would have had a much more pleasureable dive.
The wrecks are only 30-40 minutes from shore. There are lots of places to stay and lots of Key vibe restaurants/bars.
We have never been to the Keys in May. i would just check weather history and make a call if that is the right time for you. Weather is always the grand mystery that cannot be controlled or predicted with great accuracy.