5. In rectangle $A B C D$, $A B=56, A D=35$. Using lines parallel to $A B$ and $A D$, it is divided into $35 \times$ 56 unit squares. The number of unit squares that are internally crossed by diagonal $A C$ is ( ) .
(A) 84
(B) 85
(C) 91
(D) 92
5.A.

Take $A$ as the origin, the lines $AB$ and $AD$ as the $x$-axis and $y$-axis, respectively. Apart from the coordinate axes, there are 35 horizontal lines and 56 vertical lines. The diagonal $AC$ intersects with each of these lines, resulting in $35+56=91$ intersection points (including coincident points).

Next, calculate the repeated points. Since $C(56,35)$, the greatest common divisor $(56,35)=7$, the intersections of horizontal and vertical lines $C_{k}(8k, 5k) (k=1,2, \cdots, 7)$ lie on $AC$. Therefore, the different intersection points of the grid lines on $AC$ are $91-7+1=85$ (including the origin $A$). These points divide $AC$ into 84 segments, each passing through a small square, totaling 84 small squares.