Solve $x^{2}=25$, where $x$ is a real number. Simplify your answer as much as possible. If there is more than one solution, separate them with commas. If there is no solution, click on "No solution".

Step 1 ：The given equation is a simple quadratic equation, $x^{2}=25$, where $x$ is a real number.

Step 2 ：The solutions to the equation $x^{2}=25$ are the square roots of 25.

Step 3 ：Since the square root of a number n is defined as a number that when squared gives n, the solutions to the equation are $x=\sqrt{25}$ and $x=-\sqrt{25}$.

Step 4 ：The square root of 25 is 5, so the solutions are $x=5$ and $x=-5$.

Step 5 ：Final Answer: The solutions to the equation $x^{2}=25$ are $x=5$ and $x=-5$. So, the final answer is \(\boxed{5, -5}\).