Let R = the number of red marbles at the beginning.
Let B = the number of blue marbles at the beginning,
Let x = the the number of blue marbles exchanged for red marbles.  <--the answer
There are R+B marbles at the beginning and at the end.  
The given information 



R, B, and x are all positive integers.

Since  B is a multiple of 7, say B=7p, where p is a positive
integer.
Then 
or R=5p








So p must be a multiple of 3, say p=3n, where n is a positive integer.






So every solution in integers is of the form.



You did not list the possible choices, but all you have to do is look for x
being a multiple of 5.

Let's check the smallest possible solution where n=1. B=21, R=15, x=5

That checks because 15=(5/7)(21). Now there are R+B=21+15=36 marbles total, before 
and after the swapping is done.

When 5 blues are swapped for reds there are 21-5=16 blues and 15+5=20 reds,
and indeed, 20 = (5/9)(36). So that checks also.

Edwin