Max said that 36,594 is less than 5,980 because 3 is less than 5 describe Max's error and give the correct answer

Max is simply incorrect because he's stated his inequality in the opposite fashion that he should have:

36,594 is greater than 5,980

because the 3 in 36,594 represents the ten thousands place and the 5 in 5,980 represents the thousands place (which is a power of 10 less than the ten thousands place)

3 is less than 5 but 36,000 is bigger than 5,000