I would recommend you to make your application as if you were going to visit Quebec just for 2 weeks, once you’re in Canada you can stay a maximum of 6 months or you could ask for extension once you’re here in case you need it.
5 months is a lot, Ircc might think your purpose of travel is not tourism. You would have to prove you have enough money for accommodation, food, transportation, flights and for general activities as a tourist. And trust me, that’s not cheap for 5 months.