My son is 5 weeks old and is usually a good baby but sometimes he cries when he is tired or when I put him down. My mother in law said I should let him cry so that he doesnt get into the habit of me running to him and holding him all the time. I dont think this is good for him at all. Whats your thoughts on this??
Re: Allow newborn to self soothe or should I comfort??
This. PLEASE comfort that poor baby.
I think if your newborn has all his/her needs taken care of, has not been extra fussy that day (so you know they are feeling well), & is full then letting them cry a little bit is okay. I wish I would have done this more with my DS (who is now 4). He has always had an extremely hard time putting himself to sleep. I wouldn't let it do on for very long, but set an amount of time you are comfortable with. & if the cries start to sound different then you can go and check on them, lay your hand on them for comfort.
It's all about being able to understand what your child needs! My son def did develop a bad habit of needing to be rocked, or lay with someone until he falls asleep & it's a very hard one to break! I think your MIL had good advice & I know this is what my mother did with us as well. Just use your own judgement when it comes to advice
Landon & Porter
1-10-07 & 5-11-11
For a 5 week old, being comforted by his mother IS a need.
This. Get to know your child. It took me four 4 weeks to learn their cries and still dont know WHY theyre crying all the time. One thing I always tried to do and still try to do is put my babies down to sleep when they are still awake...
https://www.babycenter.com/404_how-do-i-teach-my-baby-to-soothe-himself-to-sleep_1272921.bc
This has great advice & is what I was meaning
It does recommend you wait until 3 months before you encourage them to self soothe, so I may have been wrong about doing it now, my point was that eventually (from my experience) you may want to consider this. 
Landon & Porter
1-10-07 & 5-11-11
Follow LO's lead and if he's crying, he's not self soothing!
My LO couldn't self soothe at 5 weeks- no way! Now, at 11 weeks, if she wakes up in the night she will sometimes open her eyes, grunt a little, and then go back to sleep. In my mind, this is self-soothing and I let her do it but get her as soon as she cries. She's learning how to put herself to sleep, basically, but I don't let her cry. Also, I will put her down awake now (which never worked until recently) and she can fall asleep that way. Again, if she cries I pick her back up and comfort her before trying again.
That's a good article for an appropriate age, but OP was asking for advice regarding a 5 week old, not a 3-6 month old.
From the article:
"What happens if you've given your baby plenty of chances to self-soothe and he just can't seem to do it? Take a step back and try to figure out why. Perhaps he's simply too young and doesn't yet have the developmental ability to self-soothe, just as a 3-month-old can spend hours on the living room floor yet still won't be able to crawl .In this case, wait a few days, weeks or even months before trying again."
Comforting your child when he cries at 5 weeks does not mean you will be doomed to rock him to sleep until he leaves for college... it means he needs you now. You have plenty of time to teach good sleep habits at a more developmentally appropriate age.
well said
Exactly this.
The Mouse ~ 06.12.08 | The Froggy ~ 02.23.11