Gosh, this is a tricky one and will take some courage from you.

It seems as though your neighbor doesn't realize that the alarm clock is going off, so you can frame your conversation in terms of "do you know where that noise is coming from?" if you want to be gentle.

I think that you are in a good, non-confrontational position since you already know the neighbor and have chatted before. So, next time you see each other, or if you knock on the door during the day, you could say, "I'm really sorry to bring this up, but this morning I heard an alarm clock at 5:00am which sounded like it was coming from your apartment. Would you mind turning it off or moving it somewhere else?"

I had a neighbor knock on our door a few years back. Said we had an alarm clock that was waking him in the morning. I told him, no, we didn't have anything, because if we did, *I'd* be waking up. Turns out the noise was coming from his apartment, but didn't realize it.

I'm not saying the alarm clock is on your side of the fence. I'm just saying that he asked me about the alarm clock and there was no ill-feeling or "how dare you" from my side. It's a natural thing to investigate if there's a problem, even if it means to ask a neighbor. I think anyone but some aggressive, recluse would be ok to talk to about finding the offending noise.

Good luck!

I would tend to follow Z's advice.  Maybe ask him if he knows what this constant ringing is at 5am and has he heard it?  Do not refer to an alarm clock and maybe replace 5 am with early morning - that way you are not specifically blaming him.  It could be coming from a flat above.  It is also strange that it not waking up his kids.

Alternatively ask other neighbours if they have heard it

Just approach him and be honest.... tell him how much you like him as your neighbour but ask him if he can turn his alarm clock off after he wakes up every morning because it keeps you awake.

A little honesty goes a long way.

Thanks y'all for your suggestions! I haven't actually heard the alarm since that morning, so perhaps my gentle knocks on the door have been enough, or they've been on holiday since.
For sure, if I hear it again, I will approach him that afternoon/evening.

Yes, agree it's better to ask him in person, do not leave him a note, some can respond very badly to notes..

Haha reminds me of the campaign that was going on in Geneva last year:

"Entre voisins, moins on s'entend, mieux on s'entend"