OK, I believe that I have what is very close, if the not exact number of terms that sum up to multiples of 5, or are all divisible by 5 for all 10-digit numbers. The sequence is somewhat like arithmetic series, but not exactly due to sums that are multiples of 5. For example, your series begins like this:
1000000004 , 1000000013 , 1000000022 , 1000000031 , 1000000040 , 1000000049 , 1000000059 , 1000000068 , 1000000077 , 1000000086 , 1000000095 , 1000000103 , 1000000108, 1000000117........etc.
Notice that the difference is 9 up to the 7th term. But the 7th term itself has a difference of 10 from the
previous term due to the peculiarity that the sum of the digits must be a multiple of or divisible by 5. However, that is not going to change the total number of terms of the entire sequence. And that total is the difference between the last term and the first term, or:
9,999,999,999 - 1,000,000,004 =8,999,999,995 / 5 + 1=1,800,000,000 terms, which is the best I came up with.
The sum total of 1,800,000,000 terms came out to =
9,899,999,999,100,000,000