What is the remainder of the sum of the 2005 power of 2004 plus the 2004 power of 2005 divided by 5

What is the remainder of the sum of the 2005 power of 2004 plus the 2004 power of 2005 divided by 5

The last digit of any number is bound to turn every four times
Only the first,2005/4... 1. So the last bit is the same as the first power of 4
The latter is a multiple of five.
So the answer is 4.

The last digit of any number, every four times, must be a cycle.
Only the first,2005/4... 1. So the last bit is the same as the first power of 4
The latter is a multiple of five.
So the answer is four.

(1/2004 -1)(1/2003 -1)(1/2002 -1).(1/1001 -1)(1/1000 -1) (1 In 2004 minus 1)(1 in 2003 minus 1)(1 in 2002 minus 1)...(1 in 1001 minus 1)(1 in 1000 minus 1)

(1/2004 -1)(1/2003 -1)(1/2002 -1).(1/1001 -1)(1/1000 -1)
=(-2003/2004)(-2002/2003)(-2001/2002)...(-1000/1001)(-999/1000)
=(-1)^1005*999/2004
=-999/2004