To find the number of sides of the polygon, you can use the following formula for the sum of interior angles in a polygon:

Sum of Interior Angles = (n - 2) × 180°

Where "n" is the number of sides of the polygon.

In this case, you are given that the smallest angle is 120°, and the common difference between the interior angles is 5°. So, you can set up an arithmetic progression (AP) to find the sum of the interior angles:

First angle (a) = 120° Common difference (d) = 5°

The sum of an AP is given by:

Sum = n/2 * [2a + (n-1)d]

Now, plug in the values:

Sum = n/2 * [2(120°) + (n-1)(5°)]

Simplify:

Sum = n/2 * [240° + 5°(n-1)]

Sum = n/2 * [240° + 5n - 5°]

Sum = n/2 * [5n + 235°]

Now, you know that the sum of interior angles of the polygon is equal to (n - 2) × 180°:

n/2 * [5n + 235°] = (n - 2) × 180°

Now, solve for "n":

n[5n + 235°] = 2(n - 2) × 180°

5n^2 + 235n = 2(180n - 360)

5n^2 + 235n = 360n - 720

Rearrange:

5n^2 - 125n - 720 = 0

Now, you can solve this quadratic equation for "n." You can either use the quadratic formula or factor it. Factoring, you get:

(n - 9)(5n + 80) = 0

Setting each factor equal to zero:

1. n - 9 = 0 => n = 9
2. 5n + 80 = 0 => 5n = -80 => n = -16 (but this doesn't make sense in this context)

So, the number of sides of the polygon is 9.