I've had craniosacral work done on myself and also on my daughter after she was born. With babies, it's usually most helpful when there are some obvious issues with pain or range of motion, usually due to being oddly positioned in utero or being stuck in a funny position for awhile during birth. Those babies often seem to be in some sort of discomfort, turn their head to only one side, have trouble latching, just generally seem uncomfortable and out of sorts. We had it done because I had a lengthy 2nd stage of labour (4 hours of pushing and she had been back to back, so was in kind of a funny position for awhile) and she tended to favour turning her head only to one side. She also had lots of latching issues (though I don't think that really had anything to do with it as that was mostly down to structural issues with her mouth, lip ties, etc.). Anyway, I don't really know if it made much difference but it did help her to have more range of motion in her neck, though latch wasn't much improved because of the above. It didn't make any difference on how much she needed to be held and constantly with me though, because well, that's just babies.
I would say though that unless he seems in pain, it's probably not going to make much difference to him wanting to be close to you. That's just how they are and they are designed to do that. I think mine was put down for about 20 minutes to sleep once in the first 3 months, otherwise she never slept without me, slept in the wrap, bedshared at night, was always held. That's very normal for a 5 week old. If you don't have unlimited funds and it will be a financial stretch to have the craniosacral work done, I would probably invest that money in something more likely to benefit you long term, like a wrap. A wrap was literally a lifesaver. It meant I could do things around the house, use the toilet, make lunch, sit down and relax while she napped, etc. and she slept much better with me that with me fighting to get her to sleep somewhere else. It meant bedtime was easier and we got a lot more sleep at night after about 6-8 weeks. Before 6-8 weeks, it's pretty much a blur for anyone and it sounds like you're doing a great job. It's just hard and you can't really put them down easily. If he will sleep on you, do that. Bring your lunch next to you and eat while he sleeps. Hand him off to your partner when he gets home if you need to cook or something or have him do everything around the house. It will get easier.
