Let there are n sides in the polygon.

Given smallest angles of the polygon is 120.

The difference between any two consecutive interior angles is 5.

So this forms an arithmetic series where

a = 120 and d = 5

Now sum of  all interior angles of the polygon = (2n-4)*90

=> (n/2)*[2a + (n-1)*d] = (2n-4)*90

=> (n/2)*[2*120 + (n-1)*5] = (2n-4)*90

=> (n/2)*[240 + (n-1)*5] = (2n-4)*90

=> (n/2)*[240 + 5n- 5] = (2n-4)*90

=> n*[245 + 5n] = (2n-4)*90*2

=> 5*[49n + n² ] = (2n-4)*180

=> 49n + n² = (2n-4)*180/5

=> 49n + n² = (2n-4)*36

=> 49n + n² = 2n*36 - 4*36

=> 49n + n² = 72n - 144

=> n² + 49n  - 72n + 144 = 0

=> n² + 49n  - 72n + 144 = 0

=> n² - 23n + 144 = 0

=>(n - 9)*(n - 16) = 0

=> n = 9, 16

when n =16 then largest angle of the polygon = a + (n-1)*d

                                                                   = 120 + (16 - 1)*5

                                                                   = 120 + 15*5

                                                                   = 120 +75

                                                                   = 195

Which is not possible.

So number of sides in polygon is n =9