D0n,
Up front, I'd say you'll probably only be able to get one good short out with $5k, especially if you have other gear to buy.
Next, what do you want to shoot? A narrative film or documentary. A good doc may take longer than 3 months if you aren't up to speed on what the subject is. A narrative is workable obviously, but you'll need time to develop the script. If you're not up on going from premise to treatment and then to script, that whole process will take more than 3 months as well.
Another major factor is how long a piece are you looking to do? For a narrative script 1 page equals out to around 1 minute of screen time. Add in additional camera angles or sequences other than what you story-boarded for, and add an additional 30 seconds per addition. Factor in stuff that gets cut out or put in during the edit and your flick can under or overshoot your estimated project length by a fair amount of time.
Concerning what subject you should go with, I would elaborate on Earl's suggestion by saying go with something that interests you. Whether narrative or doc, the subject's got to have you hooked from concept to distribution. That passion for the subject will lend itself to the project and will help keep you focused on getting it done.
With that in mind, remember to keep your 'producer hat' on at all times. Whatever you decide to make time, money and resources will be critical considerations. $5k may seem like a lot, but you can burn through that in a ridiculously short time. Remember, you're going to have to pay something to get your flick made.
As a first-time film-producer (you're a filmmaker after your film gets made) you must implement the KISS Program (Keep it Simple Stupid) during all phases of your project. If you don't time, money and resources are guaranteed to be wasted. So you may want to do an action film, that's fine. But recognize you won't be able to do any complicated fight scenes or car chases. Also any genre of film that relies on VFX is out because unless you can do them yourself in a timely manner, you'll have to get someone who can. Even if you can, they may not be able to meet your deadline (especially if you're not paying them!)
So, you'll have to tailor your script or doc for a micro or small crew, you'll need some place to shoot it (locations) and you'll need on-camera talent. For a narrative, you'll need actors. Now if you don't pay your crew or actors, you have to feed and house them while they are working. If they live in your town or nearby, that's good long as they can make cast/crew call on-time.
So that's a sample of what you'll run up against. You've got a serious timeline to get everything done, but I've done it in that time frame and shorter. Long as you have a solid script or doc outline and keep yourself active and efficient while working on the project, it's more than possible for you to do so with so short a window.