The OP never asked about money, but given the discussion, here's my take.
Bike commuting is like home gardening. You might think you are going to save a lot - but you don't. You start off like I did with essentially a new hobby and the sudden need to acquire a bunch of stuff. You find out that a bike will never compare to replacing a primary car. It will at best compare to replacing an old beater second car in the family. Replacing that second car isn't nothing, of course, but bike miles cost money, too.
Getting back to the garden, you are in the red for seeds, fencing, and everything else before you ever see one vegetable. And the vegetables you get come at the exact time when the store price is the least. Of course, if you commit to it, you can plant your own seeds and buy your own canning supplies, and do everything else just right and eventually start to come out ahead. I'm not going to hazard a guess whether bike commuting or home gardening is better for your health or budget.
One certainty of bike commuting is a constant drip of tiny expenses versus the constant fear of major repairs. With a commuter bike, it's always a tube, or a tire, or a lost glove, or a stretched chain, or a worn grip, or some other little $20 thing. Never a tow, alternator, or transmission for hundreds or thousands. Bike commuting is almost as easy and predictable to budget as taking the bus.
Also, while cars get into more expensive repairs as they age, bikes in some ways get cheaper. You only need to buy a multi-tool or a cable cutter once. You learn how to do more things yourself because you don't want to walk and your local bike shop is closed Mondays. You replace a sketchy part with a good part and you will be fine for thousands of miles.
With regard to the OP's question about 5 miles, I agree that almost any bike will do, provided his route is smooth (paved, boardwalk, concrete, etc) and not particularly mountainous. Five miles along a trail in the woods might change the calculus. Also, the nice thing about a shorter commute is that you can always stretch it out.