Find the equation of the circle whose radius is `5` and which touches the circle `x^2+y^2-2x-4y-20=0` externally at the point `(5,5).`

Explanation

To find the equation of the circle with a radius of 5 that touches the circle given by the equation \(x^2 + y^2 - 2x - 4y - 20 = 0\) externally at the point \((5, 5)\), we can follow these steps:

### Step 1: Find the center and radius of the given circle

The equation of the circle can be rewritten in standard form. We start with:
\[ x^2 + y^2 - 2x - 4y - 20 = 0 \]
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