The 5 numbers must add up to 19 in their last digits (ones place), for example:
1+2+4+5+7=19. The reason is that we need a carry to the tens place:
1900000+ (sum of 5 digits in the 100000 place)
0190000+ (sum of 5 digits in the 10000 place)
0019000+ (sum of 5 digits in the 1000 place)
0001900+ (sum of 5 digits in the 100 place)
0000190+ (sum of 5 digits in the tens place)
0000019= (sum of 5 digits in the ones place)
2111109 = 19×111111
So:
111111+
222222+
444444+
555555+
777777=
2111109
Another example: 1+3+4+5+6=19:
111111+
333333+
444444+
555555+
666666=
2111109