A "regular polygon" has 5 sides, all of the same length.
"Perimeter" means the total distance around the figure (polygon).
Since all of the sides have the same length, 3(x - 1) = 5x - 6.
Then 3x - 3 = 5x - 6. Solving for x, 2x=3, and x = 3/2.
Then the length of one side is 3(3/2 - 1) = 3(1/2) = 3/2.
Check: Does 5x - 6 also produce 3/2? 5(3/2) - 6 = 15/2 - 12/2 = 3/2. Yes.
Thus, the perimeter is 5 times that: P = 5(3/2) = 15/2 (answer)