My breeding cages are roughly 2/3 cubic metre. Incubation I think is around 18 days. Chicks fledge between 5-6 weeks old & will be fed and 'taught' by dad how to scavenge/crack seed for another week or so (or until he really wants to breed again). When dad is wanting to breed again he may attack his male offspring and attempt to mate with his female offspring so the offspring should be removed as soon as they are independent.
How old are your budgies? Are you certain you have a male and female? - this might seem like a daft question but some mutations it is difficult to tell for sure if one is a male. They might also not be in season, female comes into season roughly every 6-8 weeks.
This may seem harsh, but if I don't have another pair who can foster the eggs, than I just get rid of them. It is kind of your own decision, but raising baby birds is hard enough when you take them after hatching. Oftentimes when the hen is being unreliable the eggs are infertile anyway.
5 months is too young. Recommended minimum age for breeding budgies is 12 months old. It is possible for them to breed younger but they are still developing and the risks to the female is monumental at this age. There is a much higher chance of her getting eggbound (if the male knew what he was doing and impregnated her). Remove the nest box and enjoy them for the next 7 months.