Answer
$\frac{52!}{(7!)^{5}.17!}$ = 69,731,208,959,821,871,249,835,089,602,560,000
Work Step by Step
We need to distribute 52 cards in six ways such that
$n_{1}$ = 7
$n_{2}$ = 7
$n_{3}$ = 7
$n_{4}$ = 7
$n_{5}$ = 7
$n_{6}$ = 17
where $n_{1}$-$n_{5}$ represent the players and $n_{6}$ represent the remaining deck
Distributing n distinguishable objects into k distinguishable boxes such that $n_{i}$ objects are in a box i can be done $\frac{n!}{n_{1}!...n_{k}!}$
Here n= 52
k= 6
So we get $\frac{52!}{(7!)^{5}.17!}$ = 69,731,208,959,821,871,249,835,089,602,560,000
