Neem is a good natural insecticide. It stops them breeding and feeding so they die off - changes their hormones. However I have no idea if it is safe around hamsters (it certainly wouldn’t be safe to eat). We used it to get rid of head lice and nits! When stepson was younger. We all got them - ugh. I remember at the time neem (shampoo) was safe for adults but not for children so wouldn’t risk it around hamsters anyway.
I hope Souffle comes along - she will know what to do (breeder). It seems to me that it’s a bit of a rock and a hard place, weighing up the risks. Red ants are bad.
There was a similar issue on here (linked below) and the owner moved Mum and babies to a new bin cage. Read to see how she did it. Some of the babies had lumps from red ant bites.
But 5 days is not very old - their eyes won’t be open yet. I think maybe try to keep the ants down as you have been doing until the hamsters are a bit older. The owner in the thread below, the hamsters were about two weeks old.
Baby hamsters and ants