Right, well, at ten days old they can't self-settle, and they don't really give off tired signs; they just fall asleep.
And most of them won't sleep alone in a bed at that age either, and that doesn't mean you're doing anything wrong.
He's tiny tiny tiny, and he's only ever known movement and warmth and your heartbeat and your sounds. To expect him to go from that straight to lying flat in a bed without any company is too much.
I don't mean he'll be a neglected orphan child, I'm not trying to make you feel guilty - certainly five minutes on his own isn't going to be harmful. I simply mean it won't work yet.
At this age, they often will only sleep on a parent because they're just a little bundle of primal instincts, and the safety of a parent is their only chance of survival pre-civilisation. If he sleeps in a bed, fine, but don't worry if he doesn't. He will, later. And he will start giving you tired signs, later. And you'll get the hang of it, and it will be fine.
But for now, just give him what he's telling you he needs - warmth and comfort and probably motion - and love him as hard as you can.
And congratulations on your new son!