The question involves the distribution of distinct objects into distinct groups.

Option 1 (90 ways): Incorrect. The formula to calculate this scenario is n^r such that n is the number of boxes and r is the number of balls. By this formula, 3^5 would be 243, which is not equal to 90.

Option 2 (120 ways): Correct. Here is the reason: There are 3 boxes, each box has to have at least one ball, hence for the first three balls, they have 3! = 6 ways to be put into the boxes. The remaining 2 balls have 3^2 = 9 choices. Therefore, there are 6*9 = 54 ways for 3 boxes and 3 balls. However, as we have 5 balls and placement of each set having same balls are indistinguishable, we solve it as distribution identical objects into distinct boxes (boxes being distinct ball arrangements here) = 5!/(3!*2!). Therefore, the total number of ways is 5!*54/(3!*2!) = 120.

Option 3 (150 ways): Incorrect. The result that this number represents does not in any way calculate the distribution of distinct items into distinct groups.