Do you mind telling a bit more about the sleep programme you finished?
I think you're right, and he's really overtired. The normal awake time for 5 months old is about 2 hours, maybe a touch more, but that is TOTAL awake time. So from a 7am start, he would need to be asleep by 9am - not just heading to the nursery to start putting him down. Also, because he is so overtired, I would try putting him down earlier for his first nap, maybe put him down by 8.45am. If he has a short nap (1.5hrs or less), he'll need an even shorter A time before his next nap.
What do you think?
Is there anything else? 3 meals a day of solids is a lot for such a young one, any chance you could cut out one of the meals and maybe fill him up on milk? When did you last try shush-pat, what happened? Have you tried PUPD with him?
((((hugs)))) don't worry we'll help you figure this out.