That 5k include lift passes?
Yep, the family deal and a 10% discount for buying them more than 2 weeks in advance meant we paid ~€150 each for them (the family deal means the adults pay the child rate of €166 instead of the adult rate of €192, then apply the 10% discount).
For us (me, wife, 8yo daughter) it was something like:-
* Flights: £350
* Rental Car: £215 (including diesel for the ~600km of driving)
* Lift passes: £410
* Ski hire: £250 (20% discount thanks to deal with accommodation)
* Lessons for MiniGB: £85 (shared 5 x 2h lessons with proper ESF instructor with her 3 cousins)
* Accommodation: £650
* Food/Drink/etc: £300
Similar for my brother but proportionally more for flights, lift passes, ski hire and lessons as he has 3 kids. Maybe a shade over £5k for the 8 of us as it doesn't include some other things like airport parking. Accommodation was the same as we just borrowed my niece to make it 2 adults + 2 kids per apartment.
Cheap/basic accommodation (self catering studio apartments with bunk beds in the hallway for the kids) and getting in early with the (Easyjet) flights (to a non-obvious destination for skiing - Montpellier) was the key, also going Sun-Sat to keep the flight costs down, still got 5 full days and one day until 1pm of skiing in (could have pushed it to 2pm as we arrived at the airport an hour before check-in opened but erred on the side of caution as the weather was changeable).
A sprawling ski area like 3 Valleys or Espace Killy would just be a waste when going with children aged 10, 8, 7 and 6. A combination of lesson timings (and having to be back at base to pick them up ~11.30am), feeding them, and their subsequent tiredness means you'd never get to explore anywhere near all of it. It's definitely on the list for when they're all older though. I love the skiing at both of them, and I do miss the long runs with lots of elevation change, the most you can do in one go is ~500m elevation drop in Font Romeu.