The answer is yes. The sum of two negative numbers is always negative.
A negative number can be thought of as debt when you think of numbers in the context of money. For example, the value -5 or negative 5, can represent the idea that you're 5 dollars in debt. If you go get another 3 dollars in debt, then you'll be 5+3 = 8 dollars in debt total. The "8 dollars in debt" is represented by -8
So this is what it looks like with negative numbers added up
(-5)+(-3) = -8
which can also look like this
(-5)+(-3) = -(5+3) = -(8) = -8