To solve the equation 240:(x-5)=2^.5^2-20, we need to simplify both sides of the equation.

First, let's simplify the right side of the equation:
2^.5^2 = 2^1 = 2

Now, the equation becomes:
240/(x-5) = 2 - 20

Next, let's simplify the right side of the equation:
2 - 20 = -18

Now, the equation becomes:
240/(x-5) = -18

To solve for x, we can cross-multiply:
240 = -18(x-5)

Distribute -18 to the terms inside the parentheses:
240 = -18x + 90

Move -18x to the left side of the equation by subtracting 90 from both sides:
240 - 90 = -18x

Simplify the left side:
150 = -18x

Divide both sides by -18:
150/-18 = x

Simplify the left side:
-25/3 = x

Therefore, the solution to the equation 240:(x-5)=2^.5^2-20 is x = -25/3.