What changed? If you had a son born on November 15, 2013 and someone asked you today, "How old is your son?" Would you answer "My son is 5 years old." Or, "My son is 6 years old." If you are calling him 6 years old when his 6th birthday is still 9 months away, then something is wrong.
That would be true if somebody asked how old the PS4 was. They're talking about which year it's in though, different question, different answer.
As for your example, that kid would be in his 6th year. 5 years old, but in his 6th year.
1st year: 15/11/13 - 14/11/14
2nd year: 15/11/14 -14/11/15
3rd year: 15/11/15 -14/11/16
4th year: 15/11/16 -14/11/17
5th year: 15/11/17 -14/11/18
6th year: 15/11/18 -14/11/19