Answer
$1.9\times 10^{22}$ electrons flow through the hair dryer in 5.0 minutes.
Work Step by Step
We can find the charge that flows in 5.0 minutes:
$Q = I~t$
$Q = (10.0~A)(5.0\times 60~s)$
$Q = 3000~C$
We can find the number of electrons:
$\frac{3000~C}{1.6\times 10^{-19}~C} = 1.9\times 10^{22}$
$1.9\times 10^{22}$ electrons flow through the hair dryer in 5.0 minutes.