Hello and welcome to BW forums
Whilst it might not feel like you are making progress it does sound like you are doing brilliantly!
5 wks old is so tiny and of course he would rather be in your arms for the entire nap but through shush/pat and comforting him each time he cries out and then returning him to his cot you will be gradually teaching him that you are right there, that you will always return when he needs you and that it is safe to fall to sleep alone (eventually). It is a gradual process though and Tracy said to keep expectations low.
What you might try is when you put him down to keep your hands firmly on him and continue to shush/pat for an additional 20 mins until he is in deep sleep. This was Tracy's advice for the early days. If/when he screams but is so tired that he is falling to sleep the second you pick him up you might use firms hands so he feels you and pick him only slightly from the mattress rather than lifting all the way up into your arms - if he is not settling at all then of course do pick him right up, but sometimes the brief feeling of your hands and his own weightlessness as you lift him slightly may be enough to reassure him and you can gradually get him down in the cot.
If you want him to sleep on his back (I would as it is the SIDS guidance) then I would only briefly let him relax on his side as part of the soothing and aim to teach him to sleep on his back, it is not likely to happen immediately, these things take time. I remember in those early days with mine I would sometimes let him sleep on his side or tummy if it was a nap and he might have been propped with a cushion but I stayed with him throughout the nap at those times and kept a very close eye on him. For my sanity I just needed him to sleep sometimes! I didn't do this at night though he was always on his back at night.
By the way it is possible to pat on baby's hip/nappy area/tummy (not too hard) to give the patting sensation and comfort if you are finding it hard to pat on his back and then switch him to sleeping on his back.
hope this helps
