I am a whole-hearted believer in the fourth trimester - for both baby and mama! Another important thing is to get priorities straight: no disrespect to babies
but your 3 yo is the one with the big emotional needs right now, baby needs to be fed, changed, minded, held, but 3 yo needs attention. So I would put LO1's emotional needs first (and your own), and baby will be fine. A sling was a godsend to me, as was a good buggy LO2 was happy to sleep in. At 5 weeks, it's all about the cuddles, the adjustment, and you finding your feet. If everyone is fed and dressed every day, you're doing amazingly!
The first three months with two, all bets are off, enjoy it as much as you can, it's a delirious wonderful mess
naps (in the cot) are not top of the list.