The trick is to write appropriate equations and then solve the system of equations you've created.
"sum of two numbers is -5:" x + y = -5
"difference is -1:" x-y = -1
Add these two equations together. This will cause y to drop out, and you will be left with an equation in x alone:
2x = - 6, so x = -3. Subst. -3 for x in either equation, above, and find the corresponding y value.
Then write your solution as (-3, y ) (write in your value for y).