5 is fabulous

As according to basic number theory ;if any number $m$ has $2$ prime factors f1 , f2 raised to the power $a, b$ given by $m=f1^a*f2^b$ then number of factors of $m =(a+1)*(b+1)$ .

applying the same thing in the given question ;(according to the given condition ) $N=(p1)^5*(p2)^a*(p3)^b*(p4)^c*(p5)^d$

>>now for the maximum divisors the value of $a,b,c,d$ must be maximum integer value less than 5 which is $4$

$=>6*5^4=3750$ ANSWER

It is very clear to get the maximum number of divisors of this number that is: $6 \times 5^{4} = \boxed{3750}$