Here is yet another way (one function call less than the other posted
formulas)...
=RIGHT(YEAR(A1)*1000+A1-DATE(YEAR(A1),1,0),5)
And if you are willing to trade a function call for a concatenation, we can
reduce the formula by yet another function call...
=RIGHT(YEAR(A1)*1000+A1-("1/1/"&YEAR(A1))+1,5)