beginner

I'm sure you can.  Swimming is probably going to be the trickiest, so I would get as much time in on that as you can.  I'd also do something called a brick maybe once a week, which is essentially a multi discipline workout (bike to run is usually the most doable), which you simulate the actual transition you'll have to do in the race plus get used to making the quick switch from one type of movement to another.

I'd do some reading and online research (e.g. reading articles here) as well, because being familiar with the rules, strategy, and other nuances of the race is important as well.

There's tons more which I'm sure other posters will hit you with, but these are 3 off the top of my head.

Good luck

Yes, you can do one. Get yourself a decent bike and ride it rather than spin class. You've signed up for an OLY or an Olympic distance tri, when you go to talk about it. If you're military you're near a pawn shop, go look there for a road bike that fits you.

I agree with both of the above.  You need to get a bike and bike outside.  AND the swim will be the trickiest part.  How is your swimming??  If you have only been a recreational swimmer, once you try to actually SWIM a distance you will probably find it is harder than you thought.

Read up on Transitions (there are lots of resources online including youtube) T1 is swim to bike, and T2 is Bike to run.  I know on my first tri 3 summers ago I was all stressed about what to wear.  If you can you may want to invest in a pair of tri shorts.  Bike shorts that have a little bit of padding, but not too much that will get water logged on the swim or get in the way on the run.

Good Luck and I think you will be hooked!!

I'd have to agree with ^^^^  I'm not sure I understand that you don't swim but you're decent at it??  Do you mean that you know how to freestyle?  That's a good start. 

For beginners without a swimming background, the swimming portion is by far the hardest to learn.  If you haven't been in a pool (i.e. swam more than 50m in a row) in the last few months, getting up to 1500m in 5 weeks is going to be an extremely difficult task.  I'm not saying it can't be done, but you'll need 4-5 days a week in the pool at minimum.  On top of just the distance aspect, open water swimming is a different animal than swimming in the pool.  If you read this forum, you'll see 2 or 3 daily threads "Open water help!" or "I freaked out in open water!"

I don't mean to discourage you, but you've got a hefty task ahead of you.  Is there a sprint distance that you can move down to?  Just to give you some perspective, people will spend months just getting up to the sprint distance (750m), let alone the Olympic distance (1500m).