PRICE      PERSONS        COST
            100/n        n            100
            100/(n-5)    n-5          100
diffrnce       1

Let x be "the amount that each person paid after" (the unknown amount under the problem's question).


Then the original amount ("paid before") is (x-1) dollar.


The equation is


     -  = 5   people.


The solution is OBVIOUS right from the equation  x = 5  dollars.      ANSWER


CHECK.  I will check the basic equation   -  = 25 - 20 = 5 people.   ! Precisely correct !


Or, if you want to solve the equation formally, you need to reduce it to a quadratic equation and

then solve it by factoring or using the quadratic formula.