Suppose we divided N into 200 and got quotient Q and remainder 5,
like this:

    Q 
N)200
  N·Q
    5

Then to check that division by multiplying, we'd have
200 = N·Q + 5

or

195 = N·Q

So we just write down all the possibilities for N and Q,
which amounts to writing down all the ways to write 195
as a product of two positive integers:

195 =   N·Q
-------------
195 =   1·195
195 =   3·65
195 =   5·39
195 =  13·15
195 =  15·13
195 =  39·5
195 =  65·3
195 = 195·1

And of course. each of those 8 cases of N gives remainder 5 
when we divide 200 by N:

   195      65      39      15 
 1)200   3)200   5)200  13)200
   195     195     195     195
     5       5       5       5

    13       5       3       1 
15)200  39)200  65)200 195)200
   195     195     195     195
     5       5       5       5

Answer:  8

Edwin