Answer
Quotient: $x^4+x^3a+x^2a^2+xa^3+a^4$
Remainder: $0$
Work Step by Step
$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space$$\space\space$ $x^4+x^3a+x^2a^2+xa^3+a^4$
$x-a$$\space)\overline{x^5+0x^4a+0x^3a^2+0x^2a^3+0xa^4-a^5}$
$\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^5\space-x^4a}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space x^4a+0x^3a^2$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^4a-x^3a^2}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space x^3a^2+0x^2a^3$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\underline{x^3a^2-x^2a^3}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space\space\space x^2a^3+0xa^4$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space\space\space \underline{x^2a^3-xa^4}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space xa^4-a^5$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \underline{xa^4-a^5}$
$\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space \space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space\space 0$
Check answer:
$(x^4+x^3a+x^2a^2+xa^3+a^4)\cdot(x-a)+0$
$x^5-x^4a+x^4a-x^3a^2+x^3a^2-x^2a^3+x^2a^3-xa^4+xa^4-a^5$
$x^5-a^5\checkmark$
