At 5 she might be prepared to give this a go - since she's had the flu & that would leave mucus in her ,lungs which could well cause the coughing & which you need to clear - try getting a bowl of hot hot water & put in some vicks vapor rub (i don't know if you call it that, but it's a mixture of menthol, camphor & eucalyptus oils generally used as a chest rub for when you have a cold or flu) then have her lean over the bowl with a towel over her head & breathe in & out staying under for as along as she can. This clears the airways & gets right through to the lungs (if you breathe in deeply & keep doing it for - well the longer the better, but anything is better than nothing - she can come out from under the towel to wipe her face & cool off then go back under again when ready).
Do the above &/or rub some vicks on her chest, neck & back at night, oddly enough some under the feet helps alot - I have no idea why but it does!!?? If her skin is sensitive then put it on her singlet under her night top on either strap & in the middle front & back so that she still gets a fair amount of help from breathing it in, but this is mainly for at night whereas the bowl etc you can use at any time.
Good luck & I hope the new year is better than I guess your christmas is being!!