Here's what I would do:
Tell her she can have the party but only invite 10 friends max and thats the limit.
Hold it at home. Don't pay for village hall etc.
Sandwiches, crisps, chocolate fingers, fairy buns, sausage rolls - can get more than enough food for £20.
Back to basics games - sleeping lions, statues, musical bumps, pass the parcel. If nice weather, all can be played outside - if not, inside. Maybe an activity like decorate your own crown/tiara (card and glitter pens).
A few prizes - small toys/books from supermarket.
Bottle of bubbles, a balloon and piece of cake for each guest to take home.
Cost of prizes, cake, bubbles, balloons and banners - £20max.
Ask parents to stay to lend a hand.
5yo just want friends and food really - nothing fancy!