Answer
The numbers are either:
$6$ and $11$
or
$-11$ and $-6$
Work Step by Step
Let
$x$=smaller number
$x+5$=bigger number
The product of the two numbers is 66 so
$\\x(x+5)=66
\\x^2+5x=66
\\x^2+5x-66=0$
The factors of $-66$ whose sum is equal to the middle term's coefficient are 11 and $-6$.
Thus, the factored form of the trinomial is:
$\\(x+11)(x-6)=0$
Equate each factor to zero then solve each equation to have:
$\\x+11=0 \text{ or } x-6=0
x=-11 \text{ or } x=6$
Therefore the possible values of the numbers are:
$\\6$ and $11$ or $-11$ and $-6$
