When should you let the baby cry it out?

My baby is 10 days old. Sometimes he will take his passy, spit it out and cry. During the day he’s not too bad about this but at night it does it soooo much. Is this something I should let him cry out? It’s like every 5 minutes I have to get the passy for him so I can’t sleep that well. I tried to let him cry it out last night but it went on for like 5-7 minutes so I got it for him.

Update- thanks for the advise girls! I’m going to call his pediatrician in the morning about his formula. He has been spitting up recently. Maybe that’s it? Thank you!!!