.....something under 5k.
....Florida Keys reefs (1-3 miles off shore in 30-60 foot water) and scuba dive.
The boat should be at least 18 feet in length.
I do not have the time, space or patience with a cabin.
crab traps, scuba gear, research gear, kayaks, you name it....
I have yet to find a boat that doesn't have a cabin yet can still withstand the conditions off the Keys.
Okay....thinking more on this...I still believe a sailboat is a poor platform for what you want...but as Lou said to me "say oil is illegal"....and all we have are sailboats. No power boats....no gas.
Well...I would rethink the cabin thing. You don't have to use it as a cabin, but it can be a GREAT storage space for all your gear, keeping the cockpit free for operations....diving, crabbing, etc....and still provide some shelter if a shower pops up on ya.
You will need something that sits low enough in the water that you can get in/out easily. Rig a strong ladder....setup the main halyard for use as a crane to haul gear out of the water....so you're not climbing aboard kitted up. Boat must be large enough to handle offshore conditions, but in your budget this means ONLY very good weather! Also, a deep keel is out...it's the Keys and there are shallows...so a shoal draft, wing keel, or swinger.
$5k to spend....Hmmm....look around for a solid catboat. You may be hard pressed to find one in your budget, but for a sailing, working craft, they're gonna be hard to beat. Big open cockpit, decent little cabin for storage, shelter, they're built like little tanks.....nice draft with a full keel, most have small inboards.....