Hum, I may be in the far left field, but...

it's a 5 mile commute, right?

You could totally take it easy. At a relaxed pace, it will be maybe 30-45 minutes, that's not very long, and can be totally sweatless if there are no big hills and you take it easy. You can always go harder when you come back home at night.

What others said about carrying gear is great. I would avoid a backpack as much as possible, it's not very comfortable and will definitely make your back sweat. Some light panniers or just a "trunk" will probably be good enough...

I'm happy you chose a bike commute. Enjoy!