if your baby is sleeping through the night then you have no need to worry, its a good thing and means she is getting a good nights sleep and so can you! like others say you never need to wake a sleeping baby, i have heard of people waking them up at 10pm so they go through the night but i personally would never do that, they sleep through anyway if they are contented. Its ok to start some baby rice but there is no rush with solids if she is only 5 mths, they do not really need any solids until 6mths and then milk is still the most important until they are about 9/10mths. if she is hungry just increase the milk in the day instead of giving solids, 5 feeds sounds about right but if she wants more then give it until shes full.
Its so much easier to wean if you wait until they are sitting up in the highchair and can feed themselves with their fingers, just soft fruit or cooked veg to start.It saves a lot of work from pureeing and baby loves it!