General fact: 1105 is a number for which we're missing a fact (submit one to numbersapi at google mail!).
Mathematical fact: 1105 is the smallest number that can be written as the sum of 2 squares in 4 ways.
Trivia: 1105 is a boring number.
Historical date: January 9th is the day in 475 that Byzantine Emperor Zeno is forced to flee his capital at Constantinople, and his general, Basiliscus gains control of the empire.