Used to, but I'm several ankle sprains over the lifetime limit. Can't put in the training miles needed to race. Mostly cycling these days. Swim some as well, although my shoulder won't let me go more than a couple thousand meters at a time.
Cross country and track back in college, marathons, duathlons and triathlons (including several Iron distance) since.
Getting old sucks. All those injuries I powered through over the decades are catching up to me.
Anyway, if you're a competent swimmer, 750m is just about perfect warmup distance for the 5k. For best swim performance, you'd also want to get 400m in before the gun to get your heartrate and circulation up to operating speed. Assuming you have access to the water for warmups. Going from zero to fullspeed in a second is ugly and painful.
Transition? Run in your swimsuit, presumably speedo or compression shorts. No socks, elastic laces in your shoes. Lace locks are OK too if you can't find elastic laces. Tying shoes is wasted time. Talc or footpowder in the shoes if you're worried about friction. 5k is short enough that shouldn't be a big problem. Test the arrangement in a few workouts beforehand.
Be prepared for pain. At that short a distance, you're going to be in the redzone for pretty much all of it.
P.S. If you consider the swim distance a challenge, the best thing you could do is find lessons or a swim clinic between now and then. Swimming is more about technique and efficiency than anything else. Unless you were a collegiate swimmer, improving your stroke will buy you more speed than all the thousands of laps you could do between now and April.