Let the sidelengths of the smaller rectangle (in cm) be $a$ and $b$. Then the sidelengths of the larger rectangle are $a+5$ and $b+5$. The area of the smaller rectangle is $ab$, whereas the area of the larger rectangle is $(a+5)(b+5) = ab + 5a + 5b + 25$, which by the information given is equal to $ab + 100$. Thus $5a + 5b + 25 = 100$, which yields $a+b = 15$. Thus the perimeter of the smaller rectangle (in cm) is $2(a+b) = 30$.