For what a single car costs in taxes, insurance, fuel, and maintenance for a year your could get 5 used bicycles and a nice cargo bike trailer off amazon.
Are you seriously comparing a $5k car to a brand new, high quality cargo bicycle?
The equivalent cargo bike to a $5k car is below $500 and kids bicycles are below $100.
Edit: As for why I calculated like that? It is quite normal for a car to cost $5k per year. You have insurance, maintenance, repairs, taxes, financing, depreciation and fuel to pay for.
If you _only_ spend $5k on a car you're either going to skimp on a lot of those costs or pay it in maintenance, repair, and fuel... or you should compare it to the same tier of bicycles. Used bicycles you fix up yourself.
$5k for a _very nice_ cargo bike capable of transporting 1-2 kids too young to cycle on their own.
$4k for _nice_ bikes for each adult. ($2k x 2)
$3k for _good_ bikes for each kid as they grow out of the cargo bike. ($1k x 3)
$1k a year on maintenance for the bikes if you don't want to do it yourself.
$1k for locks and a crash course on how to lock your bicycles to stuff making it too much of a pain to steal.
That's $15k, or the cost of your lower end for a car for 3 years.
So between year 3 and 4 you can start either just replacing the bicycles with new nice ones because you like brand new, get yourself even more expensive electrified bikes, or spend it on other stuff.
And all the while here you could also settle for just "decent" bicycles which cost way less.
Owning a car gives you a lot of freedom and flexibility but you either live in a place that requires a car every day, or one where you need it less.
If your neighborhood is well planned, with good access to public transportation, groceries, daycare, etc. then renting a car becomes viable for the cases bikes don't cover.
Trains, trams, buses and bicycles don't need to cover every case.