Let's denote the certain number as \( x \).
According to the problem, the sum of 10 and the number \( x \) is equal to the product of the number \( x \) and 5. We can express this mathematically as follows:
\[ 10 + x = 5x \]
Now, we will solve for \( x \). Start by isolating \( x \) on one side:
\[ 10 = 5x - x \]
This simplifies to:
\[ 10 = 4x \]
Next, divide both sides by 4:
\[ x = \frac{10}{4} = \frac{5}{2} \]
Thus, the certain number is
\[ \boxed{\frac{5}{2}} \]