What is the remainder?

Your remainder can never be larger than the dividend. If you are dividing by 4, the only possible remainders are 0, 1, 2, and 3.

Your answer is wrong. The correct answer is 497 with a remainder of 2.

Yes you are wrong.
When you divide 1990 by 4 i.e. 1990/4 = 497.5
But the remainder you provide is wrong, remainder wouldn't be 5. it would be 2.

Check here,
497*4 = 1988 So the remainder would be 2

1990/4 = 497.5
The 0.5 means the remainder would be 4 X 0.5 = 2

If you divide 1990 by 4, you should get 497.5. Then, round down this number to 497. Remainder will be 2 (1990 - 497 x 4).

Hope that helps.

haha
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http://www.calculatorsoup.com/calculators/math/longdivision.php

(your remainder is 2 btw)