If it is absolutely at 5am every morning, there is another way around the problem, though it will involve some very early mornings...
Set your alarm for 4.45am and get up - let him out and sit quietly in the lounge with him - no play, dim lights etc... at first he will want to race around and play, but gradually he will learn that this is "quiet" time (and you should at least be able to snooze with him...) once this is established, gradually set your alarm 5 minutes later, though occassionally go earlier again, so that he doesn't think all his quiet behaviour is getting him left longer.... so go for 4.50am, then 4.55am, then 5am, but then go back to 4.50am for one day, then 5am, then 5.05am and so on. Don't rush this process, however tempting it may be. It might take a week at 5am for him to be calm and relaxed, but then 5.05am may only take a day....
This gets him used to the idea that you will get up even if he doesn't wake you up, and also that you getting up doesn't mean lots of fun and games and attention and breakfast, but it is actually quite boring...
We did this with Honey when she started a similar age to Bentley, as she was scratching the doors to get up from 6.15am - I was very unimpressed when I had to start setting my alarm at 6am, but we quite quickly got her into a routine of 7.15 mornings, which are managable... she sometimes lets us lie in until 7.30 at the weekends!!!!
The other thing this did was meant that when there were noises which had previously startled her and caused her to want our attention, she was able to get used to them and not react (there is a dog a few doors up who often barks in the garden at 6.30ish... she used to join in, but doesn't now...).
Good luck!