Agreed.

2222%7=3
2222*3%7=2
2222*2%7=6
2222*6%7=4
2222*4%7=5
2222*5%7=1
2222*1%7=3

So our series is 326451. Now 5555%6=5. So the fifth number is 5.

5555%7=4
5555*4%7=2
5555*2%7=1
5555*1%7=4

So our series is 421. Now 2222%3=2. The second number is 2.

5+2=7. 7%7=0, so 2222^5555+5555^2222 is divisible by 7.