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Suppose $x$ be a number of the students who have decided that they will go for a picnic.

Let each student will contribute to $y$ Rs to the total sum of $500$ Rs.

So we can write this way; $x * y =500$  $---------(1)$

Now then $5$ students have decided that they will not go for a picnic.

So, $(x-5)*(y+5)= 500$

      $xy + 5x -5y -25 = 500$

     $500 + 5x -5y -25 = 500$

     $x - y = 5$ $------------(2)$

On solving $1$ and $2$ ;

 we get $x =25$ but $5$ students did not got for picnic, So only $20$ students go for picnic..

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