My Naughty Little Sister has been a great favourite with all of mine - either Book People or Red House has the set on offer at the moment too. The Mr Gum books are good, but very silly - so it depends on whether she could cope with the sheer level of nonsense involved which can be a problem for those children who interpret things literally. The Daisy books by Nick Sharrat are good and also Junie B Jones, a kind of modern American Naughty Little Sister.
If she likes silly, there are also the Seriously Silly stories and something called Too Ghoul for School (also on offer at Book People atm I think) which my very silly DD and her very silly boyfriend like. (They are 7 but the books would be fine for a 5 year old good reader I think.)