At 5 weeks old just follow the baby's lead.
Truly following baby's lead iactually requires more thought than you would expect with a new baby, with it being such a uniquely special time. Especially so with your first baby.
Newborn babies (in the fourth trimester, as you mention) don't really spend any significant time awake. Like when in the womb, their passive state is sleeping and will only be woken for a need - hunger (needs a feed), uncomfortable (needs a nappy change or too hot/cold) or in pain. Then when waking, may only spend short times awake - like 20 or 30 minutes before returning to their passive state.
I say about requiring more thought than you might expect to follow a newborn baby's lead because it is all too easy to want to spend your days interacting with baby. Visitors wanting to hold baby, you wanting to coo over baby and so on. In actual fact most of baby's awake time will be taken with a feed, nappy check and then more-or-less straight back to sleep.
Lots of newborn issues arise from over-tiredness because parents are forgetting that baby's passive state is not awake (like them), it is asleep.
In terms of mirroring what life was like in-utero for the baby, newborns naturally like a tight, secure, enclosed feeling of being tightly packed in the womb space. This is why baby likes being held. Swaddling creates a similar effect and aids 'putting baby down' (if you so wish). There are also mattresses you can get to mirror the enclosed feeling - sleep pods.
Likewise babies are soothed by movement, like when you were walking and baby was inside you swishing around. Hence rocking, bouncing, jiggling helps baby sleep.
Finally, as you have found, babies are naturally soothed by sucking so a dummy can help. Dummy use is also shown to reduce SIDS risk in babies.