At only 5 miles, I'd be at work in maybe 10 to 15 minutes.
I live 4.4 km from work. I can bike there in maybe 10 minutes (I've biked there lots but never actually timed it), but then I have to either stand around for 15 minutes to cool down, or hop in the shower before I can go to the office. Realistically, my 10-minute bicycle commute takes a minimum of 30 minutes.
Then there's winter. Last night we got 30 cm of snow. Last week we got 20 cm of snow. Two weeks ago we got 20 cm of snow. I have studded tires on the bike, but you just can't keep those things rolling in more than about 5 or 6 cm of soft snow. Even on packed snow or ice, you're looking again at double commute time, plus snow pants, goggles, etc. Add to this the time it takes to clean and maintain your drivetrain on a daily basis due to slush and sand.
So yeah, biking to work is an option, and one that I have used, but to say that it's basically equivalent to driving for any commute over about 1 km is not being realistic in my experience.