Write the equation of a circle with a center at (-5, -5) and a diameter of 13.

The equation for a circle with center at coordinates (h,k) with radius r is:
(x-h)^2+(y-k)^2=r^2
Substituting in your values we get
(x+5)^2+(y+5)^2=6.5^2
Using foil you can expand it to:
x^2+10x+y^2+10y+50=42.25
Subtract 50 from both side to get:
x^2+10x+y^2+10y=-7.75

Final
(x+5)^2+(y+5)^2=6.5^2
Or
x^2+10x+y^2+10y=-7.75
Hope I helped :)