#### Answer

irrational number; real number

#### Work Step by Step

RECALL:
(1) $\pi$ is an irrational number.
(2) The product of a rational number and an irrational number is an irrational number.
(3) All irrational numbers are real numbers.
Thus,
$\dfrac{4\pi}{5}$ is both an irrational number and a real number.