Do you go to a Y, or is it a private company? Our YMCA opens at 5:30am and closes at 11pm.
Found one other gym that's open 5 to 11, and they cost the same per month if you commit to a year ahead of time. Also let you do a trial membership, which might be worth trying.
On the downside, they're about three doors down from the coffee shop I like (really good mochas and pastries), so I could quite easily mess up any exercise benefits. ;-)