@atomik,
It's really individual. There isn't one set number of hours that works for everyone -- some people need more, and some less, in an approximately 7-9 hour range.
Part of what is needed is REM sleep, which is hard to get if you break things up too much.
Have you actually tried napping yet?
When I have tried that in the past, I have a much harder time going to sleep at night. (So in your example, I'd wake up at 5 AM, nap 4-5 PM, then try to go to sleep at 11 -- and fail. Then I'd eventually go to sleep at midnight say, wake up at 5 AM, be wrecked, then make it to the naptime at 4 PM and pass out. Either I then stay asleep, ignoring the alarm, and wake up at 8 bright-eyed and bush-tailed but not ready to go back to sleep until 2 AM, or I successfully wake up at 5 PM but am still wrecked. Etc.)