Evaluate the expression when$x=-5\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}y=-3$.

$x+y$

Rule: The sum of any integer and its opposite is equal to zero.

Rule: Adding two positive integers always gives a positive integer; adding two negative integers always gives a negative integer.

Rule: To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

To add two numbers with the same sign, first add the two numbers and then put their common sign before the answer.

To add two numbers with the opposite sign, and subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

To evaluate the expression,$x+y$ substitute the value of x as negative 5 and y as negative 3 and add the numbers as shown below,

Rule: Adding two positive integers always gives a positive integer; adding two negative integers always gives a negative integer.

$x+y\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}when\hspace{0.17em}\hspace{0.17em}}x=-5\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}y=-3$

$\begin{array}{l}x+y\\ =-5+(-3)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Substitute\hspace{0.17em}\hspace{0.17em}the\hspace{0.17em}\hspace{0.17em}value\hspace{0.17em}\hspace{0.17em}}x=-5\text{\hspace{0.17em}\hspace{0.17em}and\hspace{0.17em}\hspace{0.17em}}y=-3\\ =-5-3=-8\\ x+y=-8\end{array}$

Thus, the value of the expression is$x+y=-8$