Hi Marc - When I'm dealing with tasks like this, I find it much more logical and easier to think in terms of the dimensions of everything in pixels, not in physical units such as cm or inches, at least when initially trying to diagnose such a problem.
The reason is that comments like your statement: "...only issue is that his scans had a print size of 100x100 cm..." doesn't directly tell me if something might have happened to the component images between your source scanning the original art work at 300 dpi (which sounds very reasonable) and the step at which your problem occurred.
In contrast, if you had noted and reported the dimensions *in pixels* of a component image immediately before resizing, we would now have a much better picture of what might have happened during your resizing step.
Anyway, to move the conversation along, I'm going to assume that immediately before the problematic re-sizing step, you were still working at the full resolution of the scans of the component images (ie, each is 12 inches multiplied by 300 ppi = 3600 pixels square), and had not done anything to reduce that. Before going on, please check and let us know if that that is the case. In other words, let's be absolutely sure that the problem didn't occur at some point before the resizing step.
You stated that the dimensions (in inches) of your final product needs to be 10" by 5" (ie, 50 square inches). The area of each component image is 12" x 12" = 144 square inches, and there are 50 of them, so that means that the total area of all of the component images is 7200 square inches. This means that you have to reduce each of these by a factor of 144x in area to get them all to fit in the assigned space. Therefore, the amount of detail in each of the component images will be greatly reduced.
This best-case reduction in detail isn't even a matter of photoshop technique, just simple geometry. Of course, there are better and worse ways to change the size of an image, but the very best you will ever be able to do (given the constraints you mentioned) is reducing the detail by a factor of 144. Other re-sampling algorithms (eg, nearest neighbor) will reduce the detail by even larger factors, but I'm assuming you are probably using one of the standard / default resampling algorithms like "bicubic (automatic)" or simple "bicubic".
HTH,
Tom M
PS - BTW, depending on how you are going to have the final product printed, you may need it's ppi to be even higher than the 300 ppi value that is typically used for high quality inkjet printing. For example, if you are having lots of copies printed on a high volume offset press, you will need more like 600 - 800 ppi to get a nice looking final product.