5-D Cube Sum Puzzle

I decided to make a puzzle on a five-dimensional cube.   We indicate a three-dimensional cube in two dimensions by drawing and connecting two two-dimensional squares.  To get to a four-dimensional cube we do the same, simply connecting two three-dimensional squares.  Doing this one more time with two four-dimensional cubes brings us to five dimensions.

I decided, for no particular reason, that we would stick to the numbers 1 through 4. Since we were already working with the number 5 in the title, I reserved one color for when the sum of adjacent entries is five or less, one when the sum was exactly six, and one when it was exactly seven.  The rest of the edges are colored in grey.  Much like my other graph puzzles, adjacent cells may not contain the same number.

Since not everyone does puzzles on a screen, sees color differences easily, or has a color printer, I created a black and white version as well.  The solution is given at a link below.

Link to Solution