How hilly is your route? 5.6 miles on a beach cruiser is easily doable. I sometimes commute to work on my Townie3 and that's 7+ or further, up to more than double, depending on which route I take. I also tow a canoe behind this bike when I go fishing. Up to 10 miles or further depending on where I'm going.

Your commute on a beach cruiser is going to be slower than on a road bike, but I have found a road bike to not be the greatest choice for commuting anyway. I would expect this commute to take less than 30 minutes, probably closer to 20 if not fighting a head wind.