From the given information we can write:

s+m+l=30 ('A triangle has perimeter of 30 inch.')

m=s+2 ('The medium side is 2 more than the short side')

l=5s ('the longest side is 5 times the length of the shortest side')

Where 's', 'm', and 'l' are the short, medium, and long sides of the triangle respectively.

Using Algebrator to solve for 'l', 'm', and 's', we get:

l=20

m=6

s=4

Therefore, the shortest side is 4 inches.