You can rephrase the question into this expression.
1/3 / 5
or
1/3 / 5/1
To divide a fraction, you simply flip the divider over (5/1 to 1/5) and switch to the operation to multiplication.
1/3 * 1/5
1*1=1
3*5=15
=1/15
If split into 5 different portions, every person would 1/15 of the potatoes.
Hope this helps!