That is exactly how I would write out that amount - and I'm fairly sure it's how you're expected to write it out on a bank cheque, at least in Australia.
Maybe this is a cultural thing. "One hundred thirty-five" sounds American to me.
In any case, both "one hundred and thirty-five dollars" and "five thousand and fourteen years" are both phrases with a single "and" before they reach some kind of dividing element that brings the number to a clear end-point.
Actually if I was reading out that number I'd say "one-thirty-five point six-seven-eight", but for formally writing it out in full.... I probably would include the "ands". It sounds wrong without them. It just needs pauses in speech, or punctuation in writing.
"One hundred and thirty-five, and five-hundred-and-sixty-eight thousandths."
The third decimal point is what makes unwieldy ("and sixty-eight hundredths" would be fine), and I don't think there is any context where you would have to fully write out a number like that.
If I was going to shorten it, I'd drop the 'hundred' as well as the 'and'. "Five-sixty-eight thousandths".
