5 week old crying himself to sleep

[LittleMissRayofHope]

I have a 5 week DS, and a 2.3 yr dd.
When I have to do things such as put dd to nap, chane her nappy, make her lunch/dinner etc I put ds in his crib and sometimes he will cry. It's a horrible sad little cry and he can turn beetroot purple - hands and everything. But after a minute, maybe 2, he will go to sleep. And often then sleep for 45 mins, sometimes 2 hours.
I know he is fed, winded and clean so he is only crying out of wanting to be held. Although he does have reflux so I'm not convo ced that it is never a bit of pain and discomfort.

Basically I'm looking for reassurance that this is fine. Never had this with dd. We were very PFB with her and almost never let her cry (for our teouble she didn't self settle or sleep through til past 1 yr old!!) so this is new to me.
I feel he is too young to be left to cry like that but at te same time I also feel there's nothing wrong with it.

Am I being unkind to my little boy??

I would never leave a baby of that age to cry, unless absolutely unavoidable. I've always picked tiny babies up immediately. Later, they do need to learn to settle themselves, but at this stage not. If really necessary though (my children weren't close in age so not a huge issue) then I don't think it will be damaging if for a very short time.