Five. (Full marks 20 points, Question (1) 8 points, Question (2) 12 points) As shown in the figure, there is a cube-shaped wire frame, and the midpoints of its sides $I, J, K, L$ are also connected with wire.
(1) There is an ant that wants to crawl along the wire from point A to point G. How many shortest routes are there? Represent these routes using letters (use the letters of the connection points passed through, for example, if the ant starts from point A, passes through point I, point L, and finally reaches point H, this route is represented as $A I L H$).
(2) Is it possible for the ant to start from point A, pass through each connection point exactly once along the wire, and finally reach point G? If possible, find one such route; if not, explain why.
(1) "The shortest path" means that the ant can neither move left nor down, otherwise it would be taking a "detour" rather than the "shortest" path. The ant can crawl on face $ABCGFE$ or on $ADCGHE$. The number of "shortest paths" on these two faces is the same, and the possible paths can be represented by the following diagram:
Therefore, there are a total of 12 shortest paths, which are:
$A B C K G, A B J K G, A B J F G, A I E F G, A I J K G$,
$A I J F G, A I E H G, A I L H G, A I L K G, A D C K G$,
$A D L K G, A D L H G$.
(2) Using the application of integer properties - coloring method or labeling method

Solution. The answer sought in the problem is impossible.
As shown in the figure, all 12 connection points are colored with black and white, and each adjacent pair of points is colored with different colors. The ant starts from the black point $A$, and must follow a route pattern like: black $\rightarrow$ white $\rightarrow$ black $\rightarrow$ white $\rightarrow$ $\cdots$, and by the 12th point $G$ it should be $\rightarrow$ white $\rightarrow$ black $(G)$, but according to the route pattern, the 12th point should be: $\rightarrow$ black $\rightarrow$ white. Therefore, it is impossible for the ant to start from point $A$, pass through each connection point exactly once, and finally reach point $G$.