5. When $a=1.67, b=1.71, c=0.46$,
$$
\begin{array}{l}
\frac{1}{a^{2}-a c-a b+b c}+\frac{2}{b^{2}-a b-b c+a c}+\frac{1}{c^{2}-a c-b c+a b} \\
=\text { ( ). }
\end{array}
$$
(A) 20
(B) 15
(C) 10
(D) 5.55
5. A.

Notice,
$$
\begin{array}{l}
\frac{1}{a^{2}-a c-a b+b c}+\frac{2}{b^{2}-a b-b c+a c}+\frac{1}{c^{2}-a c-b c+a b} \\
=\frac{1}{(a-b)(a-c)}+\frac{2}{(b-a)(b-c)}+\frac{1}{(c-a)(c-b)} \\
=\frac{(c-b)+2(a-c)+(b-a)}{(a-b)(b-c)(c-a)} \\
=\frac{a-c}{(a-b)(b-a)(c-a)} \\
=-\frac{1}{(a-b)(b-c)} \\
=20 .
\end{array}
$$