Yes you need 5 travel days.
Seat reservations for Italy can (and should) be bought on tickets.oebb.at (add Interrail/Eurail as a discount and select one-way tickets). No booking fee compared to eurail.com
- 13€ Frecciarossa trains
There is often availability the day before (unlike Paris - London)
Milan - Zurich can be done reservation-free :
- hourly RE Milan - Lugano
- any train Lugano - Zurich
Otherwise it is 11€ for the direct EC train (use tickets.oebb.at).
Suggestions :
- Bellinzona - Zurich on IR46 (or IR26 via Arth-Goldau). This train takes the Old Gotthard Railway : much more scenic than the 57-km Gotthard Tunnel.
- longer route but extremely scenic : Bernina Railway
- regional train Milan - Tirano
- Tirano - Chur either direct Bernina Express train at 14:24 (sit on the first reservation-free carriages)
- Chur - Zurich
Zurich - Paris : avoid the direct TGV, it has a 37€ seat reservation fee (2nd class) or 70€ (1st class). Itinerary that doesn't take much longer :
- Zurich - Basel - Mulhouse/Strasbourg reservation-free trains
- TGV Mulhouse/Strasbourg - Paris limited 10€, then 20€ until the train is full