Stay at home father of two here. It’s fine for babies to cry themselves to sleep. Sometimes they just need to fuss it out. As long as their not hungry, cold/hot or injured it’s perfectly ok. It’s definitely fine for a 5 month old. Just follow sleep safe guidelines and take a break from the screaming.

Also, I’m no doctor but it sounds like what you’re going through is very normal, you’re probably not really psychotic if you’re in control and you’re still connected to reality. It’s just intrusive thoughts resulting from anxiety and stress. I’d be doubtful if any parent that spends significant time with their kids claimed to never have thoughts like that. The key is finding tools to deal with the stress.