Final answer:
The equation of a sphere with a radius of 5 centered at the origin is x^2 + y^2 + z^2 = 25.
Step-by-step explanation:
An equation of a sphere with a given radius and centered at the origin can be formulated using the standard equation of a sphere: x^2 + y^2 + z^2 = r^2, where r is the radius of the sphere.
For a sphere centered at the origin (0, 0, 0) with a radius of 5, the equation is thus:
x^2 + y^2 + z^2 = 5^2
Expanding that out:
x^2 + y^2 + z^2 = 25
This equation represents all the points in space that are exactly 5 units away from the origin, forming a sphere.