Hi Natalie, I'm with PP in thinking 5 weeks is probably a little young to self-settle (unless they've been doing it all along). During the day, my DD fed then was awake a little while, then went to sleep. I used to wrap her tightly and rock her in my arms and pat her until she drifted off, then I'd put her down. If she woke, we'd try again. She would often only sleep for 45 mins at a time, but sometimes it'd be a couple of hours. It was different every day.
When she got to about 12 weeks, she wouldn't settle quickly or easily in my arms, so we transitioned to settling in the cot. I would again wrap her tightly and pat her bottom until she fell asleep.
At night we fed to sleep. I made sure the room was dark and quiet, that she was wrapped first and that everything was ready to just 'plop' her in the cradle or the cot when she'd finished. (But she pretty much always fell asleep on the boob.)
Hope some of this is helpful - I know I haven't really answered your questions, but thought I'd offer a different way of doing things in case you're interested. All the best!