The equation of ellipse is
$$
\begin{array}{l}
3 x^{2}+2 y^{2}+6 x-8 y+5=0 \\
\Rightarrow 3\left(x^{2}+2 x\right)+2\left(y^{2}-4 y\right)+5=0 \\
\Rightarrow 3\left(x^{2}+2 x+1\right)+2\left(y^{2}-4 y+4\right) \\
\quad+5-3-8=0
\end{array}
$$
$$
\begin{array}{l}
\Rightarrow 3(x+1)^{2}+2(y-2)^{2}=6 \\
\Rightarrow \frac{(x+1)^{2}}{2}+\frac{(y-2)^{2}}{3}=1
\end{array}
$$
Comparing with
$$
\begin{array}{l}
\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1, \text { we get } \\
h=-1, k=2, a^{2}=2, b^{2}=3 \\
\text { Here, centre }(h, k)=(-1,2) \\
\text { And using } a^{2}=b^{2}\left(1-e^{2}\right) \\
2=3\left(1-e^{2}\right) \Rightarrow e=\frac{1}{\sqrt{3}} \\
\text { And foci are }(h, k+b e) \text { and }(h, k-b e) \\
=(-1,2+1) \text { and }(-1,2-1) \\
=(-1,3) \text { and }(-1,1)
\end{array}
$$