Answer in two ways:

Hypothetical method:

Assuming he is all right, he should get a perfect score of 100.

If you are wrong 1, you won't get 5 points, but you will also deduct 1 points.

The actual score will lose 5+ 1=6 points.

And his actual score is 82 points, which is less than the full mark 100-82= 18 points.

18÷6=3 questions.

That is, he just made three mistakes and got 20-3= 17 right.

Equation method: If you answer the X question correctly, you will answer the (20-x) question incorrectly.

5x-(20-x)=82 gives x= 17.