How do I speed up a certain part of footage in Sony Vegas 5.0?

Right click on the clip in the timeline, go to insert envelope, and insert a velocity envelope. From there move the bar up and accordingly to how fast or slow you want it to go.

Okay, thanks.
How do I exclude part of the video so that it isn't sped up?

You can add points and adjust it to regular speed or raise the speed with in a clip. Just right click on the bar and add point.

Also, if you've sped up the video, be sure to drag the event clip length back down, or else your event will start to loop.

another way is to just split at the start and end point of the sped up/slowed down video and then hold control and drag accordingly from one end.

either works. you've got options.