5) If you divide the same number to both sides of an equation, the equation is still true. For example, if $a=b$, then $a / c=b / c$. Property:

Step 1 ：Given an equation where $a=b$, we want to prove that if we divide both sides of the equation by the same non-zero number, the equation remains true. In mathematical terms, we want to prove that $a / c=b / c$ for any non-zero $c$.

Step 2 ：This is a fundamental property of equations. If you divide both sides of an equation by the same non-zero number, the equation remains true. This is because division is an operation that is applied equally to both sides, maintaining the balance of the equation.

Step 3 ：Let's confirm this property with a test. We will use a Python code to check if the property holds true for given values of a, b, and c.

Step 4 ：The Python code returned True, which means that the property holds true for the given values of a, b, and c. This confirms our initial thought that if you divide both sides of an equation by the same non-zero number, the equation remains true.

Step 5 ：Final Answer: \(\boxed{\text{The property that if you divide both sides of an equation by the same non-zero number, the equation remains true is confirmed. In mathematical terms, if } a=b, \text{ then } a / c=b / c \text{ for any non-zero } c.}\)