4. As shown in Figure 2, in a rectangular box, $A B=5$, $B C=4, C C_{1}=3$. The shortest distance an ant travels from point $A_{1}$ along the surface of the box to point $C$ is ( ).
(A) $\sqrt{74}$
(B) $\sqrt{78}$
(C) $\sqrt{80}$
(D) $\sqrt{90}$
4. A.

From the plane development of the cuboid, the shorter routes are the three cases shown in Figure 9:
In Figure 9(a),
$$
A_{1} C=\sqrt{5^{2}+(3+4)^{2}}=\sqrt{74} \text {; }
$$

In Figure 9(b),
$$
A_{1} C=\sqrt{3^{2}+(5+4)^{2}}=\sqrt{90} \text {; }
$$

In Figure 9(c),
$$
A_{1} C=\sqrt{4^{2}+(3+5)^{2}}=\sqrt{80} \text {. }
$$

Therefore, the shortest distance is $\sqrt{74}$.