Identify the given data

We are given 5 observations: $5, 8, 12, x, 15$, the number of observations $n = 5$, and their mean $\text{Mean} = 10$.

$n = 5, ext{\text{Mean}} = 10$

Apply the mean formula

The formula for the arithmetic mean is the sum of all observations divided by the total number of observations.

$ext{\text{Mean}} = \frac{5 + 8 + 12 + x + 15}{5}$

Calculate the sum and solve for x

Multiply both sides by 5 to get the total sum, then equate it to $40 + x$ to find $x = 10$.

$50 = 40 + x \implies x = 10$