Night schedule

My baby’s 5 weeks old and we do -
Bottle at 6pm followed by a bath every other night, then a nap (sometimes the nap is before the bath, other-times after). Another bottle at 10pm, then i let baby wake me up which is usually around 2am. Then he will sleep until wake time around 6am.

What helps us is keeping our room dark and we use the Vtech Hush Lite - settings always the same, red light with a heartbeat sound. We use Mamas and Papas swaddles and have a cuddle in bed around 10mins, once asleep we transfer to snuz pod

You don't need to worry about bathing them or even having a night schedule. Just feed when they're hungry, cuddle when they want to, and sleep when you can. Look into safe chest sleeping and co sleeping if your baby doesn't like to be put down.

Your baby is so so fresh, they don't need a routine at this point, they're going through major developmental changes and growth spurts

Totally agree with Charley 😊 understandable if you'd personally like a bedtime routine, but for the baby it likely won't make any difference whatsoever, they're simply too young for it. Babies make their own routines at that age