The equation of a circle with center \((h, k)\) and radius \(r\) is given by the formula:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
For a circle with center \((8, 6)\) and radius \(5\):
- \(h = 8\)
- \(k = 6\)
- \(r = 5\)
Substituting these values into the equation, we get:
\[ (x - 8)^2 + (y - 6)^2 = 5^2 \]
Simplifying this gives:
\[ (x - 8)^2 + (y - 6)^2 = 25 \]
Therefore, the equation of the circle is:
\[ (x - 8)^2 + (y - 6)^2 = 25 \]