I am a Venezuelan citizen and an American legal resident (green card holder). I am currently in Vancouver, Canada and my passport expires on the 23rd of November 2016. Can I travel back to the US on the 13th of November? Currently, I plan to go back on the 5th of November.
You can enter the US solely on your Permanent Resident card. Only it needs to be valid and not expired. It doesn't matter when your passport expires.
From the CBP:
U.S. LPRs do not need a passport to enter the United States as per (8 CFR 211.1(a)), however, they may need a passport to enter another country.
When you return to the US, you should contact a Venezuela embassy or consulate to renew your passport, as you will probably need it to travel elsewhere in the world.
The upcoming expiration of your Venezuelan passport will not affect your re-entry into the US, whether you return on the 5th or on the 23rd of November.
Lawful Permanent Residents of the U.S. must present a valid, unexpired Permanent Resident Card (Green Card, Form I-551). While not required, it's a good idea to carry your identity document (passport, foreign national ID card, or US driver's license). You'll want to renew your passport for future travel, as the green card may not give you admission to other countries, as you know.
While they may not apply to you, if you've taken a brief trip to Canada, there are other conditions which can affect an LPR: a reentry permit can be required if one is out of the country for more than a year or, if gone for 2 or more years, a returning resident visa would be needed.