If I had a short commute like that, I would just wear work clothes. When I ride to church, a little over 2 miles, I wear my church clothes and even on hot Texas days I can get away with it.

That said, I have a 17 mile commute one way. I have a shower at work now, but last year when my commute was 7 miles each way, I didn't. I carry my clothes with me each day I ride to work. I have a rack and pannier bags. You can get an amazing amount of stuff into panniers. When I didn't have a shower available to me, I took a shower at home and freshened up using deoderant and baby powder upon arriving at work. Some people prefer baby wipes to clean up (or whatever the adult equivalent is).