Canada does not appear to have "6 month rule". From the government website:
All international travellers must carry acceptable identification and a valid visa (if necessary) when entering Canada. A passport is recommended because it is the only reliable and universally-accepted travel and identification document for the purpose of international travel.
I did a search on that whole site for "6 months" and did not find any indication of how long a passport needs to be valid for. I also checked a handful of "travel tips" articles that mentioned the rule and did not include Canada in the list of countries with the rule, though most such articles (perhaps all) were aimed at US passport holders, and the rule if it did exist would almost certainly not apply to US passport holders.
You can check with the Canadian ETA people directly using this form: http://www.cic.gc.ca/english/visit/eta-form-help.asp and ask them if 5 months on the passport is an issue, and if it is what that means for the ETA, but it seems to me that it won't be an issue. (I recommend you ask them anyway to put your mind fully at ease.)