What age do you transition from bassinet to crib

I'm a FTM and our LO (13 lbs, 22.5 inches) doesn't seem to fit his bassinet any longer. My hubby and I are concerned that he might be too small for the crib- his arms fit between the slats still.

Our LO is only 5 wks old but he is able to roll onto his side and push against the mesh sides of the bassinet. When I lay him on his back, he stretches his arms and legs automatically. If his hands touch the mesh he instantly wakes up and rolls on his side to play with the mesh- poking it and running his nails against it. It's hilarious when it isn't midnight!

Any feedback is appreciated. Thanks!