Solution :
Suppose the ellips equation :
(x-p)^2/a^2+(y-q)^2/b^2=1
where (p,q)=its center
since the absisca of its foci equal then p=-5
q=(-8+4)/2=-4/2=-2
Its center should be (-5,-2)
2c=-2-(-8)
2c=6
c=3
2b=2-(-6)
2b=8
b=4
b^2-a^2=c^2
4^2-a^2=3^2
a^2=16-9
a^2=7
a=sqrt(7)
its solution should be :
(x+5)^2/7+(y+2)^2/16=1