I recently came across something on 23andMe that might apply and be helpful here; it's from the short descriptions of the populations they use for ethnicity (though they don't use that term). This one is for their Native American category:

"Native peoples of the Americas have contributed genetically to today's populations in North, Central, and South America. In North America, however, Native American ancestry tends to be five or more generations back, so that little DNA evidence of this ancestry remains."

Despite the fact that your 5th great grandfather's identity and relationship to you are clearly documented, according to the quote above, it seems possible that he could be just far enough back so that the amount of his DNA you possess could be too small to be detected by current testing.

I'm not sure how AncestryDNA calculates it, so it might not apply to the results here, and I'm a newbie to DNA and no expert!