If the teeth are loose than they will more than likely eventually fall out. Can you maybe wait just one more month until he is 6-months old for his neuter?
I got Riley neutered at 6 months and then ended up having to take him back 3 months later because his 2 upper canines didn't fall out... They weren't loose whatsoever and there was No Way they were coming out on their own. Well.... they charged me another almost $400 for their removal and Riley had to go under, again. I was a bit upset, to say the least.
I had just assumed they would pull any baby teeth at the time of neuter if there were any still there. That is what they did with my prior dog when I had him neutered at 6-months. I didn't even think to ask about it or mention doing it for Riley..... and I didn't even know he was still retaining two baby teeth until I dropped him off for a quick nail trim a couple months later. They brought it to my attention at that time.
When I went to drop him off for his teeth, appt. I let it be known to the tech that I wasn't happy.....I didn't even really care about the money part of it........ I was mainly upset because I didn't want Riley to have to go under "again".... and be in any discomfort. The tech confirmed that they usually pull any baby teeth that are left at the time of neuter and that this was an unusual circumstance.
All in all he came through it fine.
Good Luck!!