Think of a pie. Lemon, apple, it doesn't matter. (If cheesecake is your thing, use it.) You can slice a pie in half, in 3 equal pieces, in 4 equal pieces, in 5 equal pieces, etc. You still have one whole pie, you just divided it differently. Same amount of pie, just different number of slices.
The quarter note is the pie. The divisions are the slices. If you count 8th notes (which is a quarter note broken into 2 pieces) you would count 1 &. If you count 16th notes (which is a quarter note broken into 4 pieces) you would count
1 e & a. I'm not sure about the count names for 5's, but it would be along the same idea.
One thing you might try doing (for your break-down sake) is consider each quarter note as 1 whole measure. Clap each quarter note slowly, at a constant tempo. And while doing that count to five (using equal increments of space). Another way would be to continually count to five, and each time you get to the 1, clap your hands. Each clap would be considered a quarter note, and you have started to teach your brain how to count and separate in 5's. The next step is to turn on a metronome, and repeat the previous step (using the metronome clicks as your quarter notes, and using your sticks on a snare (or practice pad) you would count to five (with each click of the 'nome being the 1).
Someone else may have another way, but this is how I learned. I taught myself, and I teach kids (and they learn it like this, I just did it yesterday, so I know it works)
Hope this helps.
Someone else