Let  L  and  W  be the length and the width dimensions of the rectangle.

Then you are given that

 = 95,         (1)
L - W = 5.           (2)

Factor (1) as

(L + W)*(L - W ) = 95

and replace (L - W) here as 5, due to (2). You will get

5*(L + W) = 95,   or

L + W =  = 19.    (3)


Now combine the two equations (2) and (3) to a system

L + W = 19,         (4)
L - W =  5.         (5)

Add the equations (4) and (5) to get   2L = 24,  L =  = 12.


Then from (4)  W = 19 - 12 = 7.


Answer.  The dimensions are  12 cm  and  7 cm.