I don't have any experience with one litter right after another, but if you are worried about mum hurting the older babies (or the older babies hurting the younger) then I would move older babies in to a different cage. It's not ideal but as Jack's-Jane said, at 5 weeks they should be okay without mums milk but they are still very delicate so please keep them on the same dry food and hay that was in mums cage or they could become very unwell. On here you might see that it's recommended that adult rabbits only have an egg cup of dry food (or less) each day. Your female has given birth twice in just over a month and has been using a lot of her energy to make milk, I personally would be giving her as much dry food as she wants and some vegetables (not carrots) every day, but only the dry food and veg that she's currently used to, anything else should be introduced very very slowly like with the babies.
Something else that is very important and i'm going to put this in bold so it isn't missed: Rabbits can squeeze through spaces that look way too narrow for them. I put some 8 week old rabbits in a dog crate, the rabbits were at least double the width of the space in between the bars but they could squeeze through easily. So please bear that in mind, you don't want any of them slipping through the bars and ending up somewhere dangerous or back in to dads/their siblings of the opposite sex cage
I'm not sure how old you are, but when I was about 13/14 I got a female rabbit who was already pregnant. I absolutely did not want to sell the babies to strangers where they'd probably be stuck in a 3ft cage by themselves and forgotten about a month or two later or worse, used as dog bait. I made a form for potential new owners and I wanted to know how much they knew about rabbits, pictures of where they would be kept etc and only sell the babies to the most suitable people. My step-mum promised two of them to friends of hers that I've never met and I was absolutely heartbroken, almost 10 years later I still resent my step-mum for what she did and wonder what kind of life those babies had. Anyway I know it's really tough, sometimes young people have better (and more up to date) knowledge about a certain topic but parents just don't want to listen. Many people have grown up thinking that keeping a single rabbit in a tiny cage with no hay etc is normal, and usually haven't spent enough time with those rabbits to know that they have as much personality as a cat or dog but are much more neglected, so when someone younger tries to say 'actually this isn't right' or 'please can we spend money on a larger cage/vet bills' they're called ridiculous and told it's just a rabbit. I really hope you can convince your parents to either let you choose the new owners carefully or give them to a rescue. Rescues are very full but if your parents seem insistent on selling the babies off to the first few people that show up then I honestly think rescue would be a better idea, perhaps you could sell the idea to your parents by saying they can all be moved at once, guaranteed to be very well looked after until they find a new home (and rescues normally do house visits to new owners to really ensure they're going somewhere good), they can stay with siblings for longer (male/female separated of course) and you won't have to deal with strangers coming to your house to look at the rabbits. If you find a rescue nearby with space then maybe you could offer to volunteer there and give something back.
When she does it will she jump up if you disturb her with a loud noise/touch? Does she seem to be breathing at her normal rate (bear in mind a rabbits breathing rate is much higher than ours so even a relaxed rabbit can look like it's breathing a lot, it's better to compare to what she usually does)? Is she eating and drinking normally?
