Given that the circle having radius 5 touches both the coordinate axes.

Let us assume the circle touches the co - ordinate axes at (a,0) and (0,a). Then the circle will have the centre at (a, a) and radius |a|.

It is given that the radius is 5 units.

The centre of the circle is (±5,±5).

We know that the equation of the circle with centre (p, q) and having radius ‘r’ is given by:

⇒ (x - p)² + (y - q)² = r²

Now we substitute the corresponding values in the equation:

⇒ (x±5)² + (y±5)² = (5)²

⇒ x²±10x + 25 + y²±10y + 25 = 25

⇒ x² + y²±10x±10y + 25 = 0

∴The correct option is (c).