To expand the expression \((2m - 5)^2\), we can use the formula for the square of a binomial, \((a - b)^2 = a^2 - 2ab + b^2\).
Here, \(a = 2m\) and \(b = 5\). Applying the formula:
- \(a^2 = (2m)^2 = 4m^2\)
- \(b^2 = 5^2 = 25\)
- \(2ab = 2(2m)(5) = 20m\)
Putting it all together:
\[ (2m - 5)^2 = a^2 - 2ab + b^2 = 4m^2 - 20m + 25 \]
Thus, the expanded form of \((2m - 5)^2\) is:
\[ \boxed{4m^2 - 20m + 25} \]