Why scan so high then print so much lower?
Because the scan resolution determines how many total pixels you pull from the film. Print resolution determines how many pixels you send to the printer.
Assuming you are scanning 35mm film you have an film image that's about 1 x1.5 inches. If you scan at 5000dpi you will have a digital image with 5000 x 7500 pixels. Note there is no set size associated with this. It's the pixel count that's important. The image file has a setting for dpi, which is used to calculate an image size by dividing the pixel dimensions by the dpi. As long as you don't resample the file it will always contain 5000x7500 pixels.
When you print this file at 300dpi it will be 16.67" x 25" (5000/300 x 7500x300). This will send every pixel in the file to the printer, no more and no less. The difference with printing is the printer needs to know how big you want it on paper. With scanning the film has a fixed size that you can't change (without using a different format).
With printing the printer will take the pixels you give it and either up or down resample the image so it has 300dpi (or some other native value depending on the printer). If you give it 300 dpi it doesn't do any resampling.