The foci of the ellipse, $25(x+1{)}^2+9(y+2{)}^2=225$, are at 

The equation can be written as 

$\begin{array}{l}\frac{(x+1{)}^2}{9}+\frac{(y+2{)}^2}{25}=1\\ C=(-1,-2),a^2=9,b^2=25,e=4/5\end{array}$

Major axis along y-axis.  

foci are (h,k$\pm be$)

Thus the foci are (- 1, 2) and (- 1, - 6).