10. (6 points) A few hundred years ago, Columbus discovered the New World in America, and the four digits of that year are all different, their sum equals 16. If the tens digit is increased by 1, then the tens digit is exactly 5 times the units digit, so Columbus discovered the New World in America in the year $\qquad$.

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【Analysis】Since it is several hundred years ago, the thousand's digit of the four-digit number must be 1. Also, the ten's digit plus 1 is exactly 5 times the unit's digit, so the unit's digit can be 1 or 2. However, since the thousand's digit is 1, the unit's digit can only be 2, and $2 \times 5 = 9 + 1$, which means the ten's digit is 9, and the unit's digit is 2. Their sum equals 16, so the hundred's digit is: $16 - 1 - 9 - 2 = 4$. Therefore, Columbus discovered the New World in America in the year 1492.

【Solution】According to the Gregorian calendar, the thousand's digit of the four-digit number must be 1,
and $2 \times 5 = 9 + 1$, so the ten's digit is 9, and the unit's digit is 2,
their sum equals 16, so the hundred's digit is:
$$
16 - 1 - 9 - 2 = 4,
$$

Therefore, Columbus discovered the New World in America in the year 1492.
The answer is: 1492.