How many ways are there to distribute hands of 5 cards to each of four players from the standard deck of 52 cards?

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The answer is $\frac{52!}{(5!\times 5!\times 5!\times 5!\times 32!)} = 1.4782628e+24$

This reminds me of that if I have to select 7 objects from 3 types with infinite supply:

oo|oo|ooo

I know that it's no necessary to use the bar in this question because each person has the same numbers of the cards, but I still want to try to add 4 bars.

That is:

5 cards for person1 | 5 cards for person2 | 5 cards for person3 | 5 cards for person4 | undealt cars

so the equation is: $\frac{56!}{(5!\times 5!\times 5!\times 5!\times 32!\times 4!)}=5.4295116e+29$

What's wrong with my idea?