#### Answer

$EB=6$

#### Work Step by Step

We are given that $AD=5$ and $DE=4$. Altitude $DE$ forms a right triangle, $\triangle ADE$. Using the Pythagorean Theorem...
$a^{2}+b^{2}=c^{2}$
$a^{2}+4^{2}=5^{2}$
$a^{2}+16=25$
Subtract 16 from both sides...
$a^{2}=9$
Square root both sides...
$a=3$ or $AE=3$
Opposite sides of a parallelogram are congruent. Therefore, $DC=AB=9$.
Using the Segment Addition Postulate...
$AE+EB=AB$
Substitute in known lengths...
$3+EB=9$
Subtract three from both sides...
$EB=6$