As CMaster indicated, an eTA is not like a visa in that you're guaranteed a certain validity before you arrive, it's merely an authorization to travel and the border officer decides how long you can stay. In theory however, you can stay up to 6 months.
This page has it quite clearly:
Your eTA authorizes you to visit Canada for up to six months or until the date prescribed by a border services officer on your arrival to Canada. If you need to stay in Canada longer, you must apply to extend your stay.
Once you have an eTA, it will be valid for five years, or until your passport expires, whichever comes first.
Note: A valid eTA and travel document (passport) will facilitate your entry to Canada. When you arrive at the border, a border services officer will ask to see your passport or travel documents and ask you a few questions.The officer will then decide if you can enter Canada.
Sure Canada eta is not a visa, but its allowing you as an EU citizen to travel to Canada by air. Normally, its valid for 5 years, but at the point of entry the office will decide if you must allowing to enter or not.
And you have right to stay not more than six months though you have five years. If you want to staying more than six months, you can extend but it depends upon your circumstances.
Eta is not a working permit nor students visa, so if you want to work you can applying for work permit and if you want to study more than six months, you can applying for study permit, but programmes less than six months you do not need study permit.