1. **State the problem:** We need to find the equation of the locus of a point $P(x,y)$ that is always 5 units away from the origin $(0,0)$. 2. **Understand the concept:** The locus of points that are a fixed distance $r$ from a fixed point (the origin) is a circle with radius $r$ centered at that point. 3. **Apply the distance formula:** The distance between $P(x,y)$ and the origin $(0,0)$ is given by $$\sqrt{(x-0)^2 + (y-0)^2} = \sqrt{x^2 + y^2}.$$ 4. **Set the distance equal to 5:** Since the point is always 5 units from the origin, we have $$\sqrt{x^2 + y^2} = 5.$$ 5. **Square both sides to eliminate the square root:** $$x^2 + y^2 = 25.$$ 6. **Final equation:** The locus is the circle centered at the origin with radius 5, so the equation is $$x^2 + y^2 = 25.$$