5. If $\triangle A B C$ is a right triangle with integer sides, $B C$ is the hypotenuse and $2 A C=B C+A B$, then which of the following numbers could be a side length of this triangle? ( ).
(A) 1993
(B) 1994
(C) 1995
(D) 1997
5. (C).

From the given conditions and the Pythagorean theorem, we have
$$
\left\{\begin{array}{l}
B C^{2}=A C^{2}+A B^{2}, \\
2 A C=B C+A B .
\end{array}\right.
$$

Solving these equations, we get
$$
B C: A C \text { : } A B=5: 4: 3 \text {. }
$$
$\therefore$ The sides of $\triangle A B C$ are multiples of 5, 4, and 3.

Among the four options, only 1995 is a multiple of both 3 and 5, while the other three numbers $1993, 1994, 1997$ are neither multiples of 3, 4, nor 5. Therefore, only 1995 can be the length of a side of this triangle.