The given equation is:

\[
(x + 5)^2 + (y - 2)^2 = 25
\]

This is the equation of a circle in standard form: 

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \((h, k)\) is the center of the circle.
- \(r\) is the radius of the circle.

### Solution:
By comparing the given equation \((x + 5)^2 + (y - 2)^2 = 25\) with the standard form, we can identify the following:

- The center of the circle is \((-5, 2)\) (since \(x + 5\) can be rewritten as \((x - (-5))\)).
- The radius \(r\) is \(\sqrt{25} = 5\).

### Summary:
- Center: \((-5, 2)\)
- Radius: \(5\)

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the graph of this circle look on a coordinate plane?
2. How do we derive the general equation of a circle from its center and radius?
3. What would the equation look like if the radius were doubled?
4. How do you find the intercepts of this circle with the x-axis or y-axis?
5. Can you explain how to rewrite this equation in expanded form?

**Tip**: When graphing a circle, always plot the center first and use the radius to determine key points along the circle.

Discover how to solve the equation of a circle (x+5)²+(y-2)²=25, identifying the center and radius. This problem covers key geometric concepts such as the equation of a circle, its center, and radius. Suitable for students in Grades 9-10.

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