5. As shown in Figure 3, there are 16 points, and the distance between any two adjacent points, whether left and right or up and down, is equal to 1. If these points are used as the vertices of triangles, then, a total of  right-angled triangles can be obtained.
5.200.

As shown in Figure 6, the number of right-angled triangles with $A$ as the right-angle vertex is $C_{3}^{1} \cdot C_{3}^{1}=9$;
the number of right-angled triangles with $B$ as the right-angle vertex is
$$
C_{3}^{1} \cdot C_{3}^{1}+C_{2}^{1}+1=12 \text {; }
$$

the number of right-angled triangles with $C$ as the right-angle vertex is
$$
C_{3}^{1} \cdot C_{3}^{1}+C_{2}^{1} \cdot C_{3}^{1}+2=17 \text {; }
$$

By symmetry, the total number of right-angled triangles is
$$
9 \times 4+12 \times 8+17 \times 4=200
$$

right-angled triangles.