New to the sport

First of all, Welcome to BT!

You have a bike so there isn't much else that you 'need'.  You'll probably see quite a few people who are doing their first race at the sprint you're planning on doing that will have mountain bikes or cross bikes just to see if they enjoy it before spending on a bike.  I would highly recommend getting a pair of tri shorts which are essentially bike shorts with a smaller pad that are made to be worn throughout the race, and a tri top although not nearly as essential.  A decent pair of running shoes are very important as well but more for training than racing. 

Myself, I've been at this for just a year now so I know what you're going through.  I had the most trouble with swimming, a half a mile seemed like an endless swim.  Since you're background appears to be a runner's, I'd spend most of the time you have in the pool.  You can obviously run the 5k and a 10.5 mile bike is probably not that hard for you either.  A sprint is short enough that nutrition won't be an issue.

Use the resources here on BT.  They were essential to me, especially the forums where you'll get lots of different opinions on everything.

Here's a good article from BT on transition areas. http://www.beginnertriathlete.com/cms/article-detail.asp?articleid=115 and a fantastic video about transition areas http://www.beginnertriathlete.com/cms/article-detail.asp?articleid=1488, it may be a little overkill but the visual really helped settle me down.

 Like I said, welcome to BT and if you have any other questions don't hesitate to PM me or post again on the NH forum.

 Good Luck!