If j and k are positive integers where k > j, what is the value of the remainder

If j and k are positive integers where k > j, what is the value of the remainder when k is divided by j?

(1) There exists a positive integer m such that k = jm + 5.

(2) j > 5

The reason is as follows:
k/j = (jm + 5)/j = m + 5/j

If 5 < j, then the remainder will be 5.
But when 5 > j, the remainder can't be 5.
The examples of gokul showed this (Thank you, gokul :D)

So, (1) is insuff.

(1) and (2) is suff.