You are solving for exponent m. Note the equal sign. What you do to one side, you do to the other.
First, divide x^3 and y^2 from both sides
x^(3 - 3) * y^(2 - 2) * ((x² * y³ * z^m)/(z^-5)) = (x^5 - 3)(y^5 - 2)(z)
(x² * y³ * z^m)/(z^-5) = (x²)(y³)(z)
Next, flip z^-5 to the numerator
(x² * y³ *z^(m + 5)) = (x²)(y³)(z)
Simplify the z
x² - x² = 0
y³ - y³ = 0
z^(m + 5) = z
z^ (-4 + 5) = z
z^1 = z
m = -4
hope this helps
