The average of 5 days he ate is: \(100:5=20\left(cookies\right)\)

The cookies he eat in 5 days has the distance: \(-12;-6;0;6;12\).

So the cookies he ate on the fifth day is: \(20+12=32\left(cookies\right)\)

Let x be the number of cookies he ate in the 3^rd day,then the number of cookies he ate in the 1^st,2^nd,4^th,5^th are x - 12 ; x - 6 ; x + 6 ; x + 12 \(\left(x>12\right)\) .We have :

\(\left(x-12\right)+\left(x-6\right)+x+\left(x+6\right)+\left(x+12\right)=100\)

\(\Rightarrow5x=100\Rightarrow x=20\Rightarrow x+12=32\)

So,he ate 32 cookies on the fifth day