If your problem is this:
(m - 2)/(m - 5) * (m + 5)/(m - 2) = -1
(m - 2) cancels out in both the numerator and denominator on the left-hand side since you are multiplying.
That leaves us with this:
(m + 5)/(m - 5) = -1
To solve for m:
Multiply both sides by (m - 5) to get rid of the fraction and make the equation easier to solve. Whatever operation you do to one side of the equation you must do to the other side as well.
We are left with this:
m + 5 = -1 (m - 5)
m + 5 = -m + 5
Add m to both sides to get this result:
2m + 5 = 5
Subtract 5 from both sides to get this result:
2m = 0
Divide both sides by 2 to get m by itself and solve the equation.
m = 0
Substitute 0 for m in the original equation to check. It always helps to check your work!