If baby is exhausted I would revert back to an awake time led routine. Take cues from your baby what that awake time is because it will depend on how exhausted he is.
My philosophy is to not keep a tired baby awake without very good reason. So in my house as soon as baby was tired, it would be sleep time pretty much straight away.
Remember that outward tired signs (ear rubbing, red eyes, yawning, drowsy eyes) mean baby needed to be sleep at least half an hour earlier. So use this to inform when you time future naps by working out how long he was actually awake from and reducing next time. The ideal situation is to predict when baby will be tired and get him down to sleep before he is acting tired.
I would try for 2h awake times initially and go from there. 10 months would also be a good age to move to cot naps in a dark room, if you haven't already.
The only awake time to make different is the one just before bed. This wants stretching a but, so if all other awake times are 2h try 3h before bed. But as I said, be guided by your baby (not me) what awake times work best for your DS.
This will require you to be more flexible with bedtime, depending on how naps have gone that day. So Do bedtime might have a 2 hour window - day anywhere between 7pm and 9pm.
Say baby wakes from a nap at 4pm, then you might go for a 7pm bedtime. But if baby is awake at 3pm then I'd go for another nap at 5pm and bedtime at 8pm, for example.
Whilst talking about bedtimes, remember than 11h overnight is average at this stage, with a 10-12h range being normal. A bedtime of 7am will give you a quote reasonable wake up time from 5am. So actually, your bedtime needs to be later if you are looking for a 7am wake up.