Question
How tall do Princess Lillies grow in zone 5 on average

Answer
Depending on the hybrid you grow, Dutch-bred Princess Lily (aka 'Dwarf Peruvian Lily' or 'Dwarf Alstroemeria') hits anywhere between 8 inches and 30 inches tall.  'Theresa' reaches 12 inches. 'Paola' is only 8 inches.  'Camilla' reaches 16 inches.  

In your Zone 5, as you probably are aware, temps get too cold for these plants to survive out of doors.  You'll need to pot them, and grow them in a Sunny window, mid-Fall through Spring. Once nights are mild enough, they can be moved outside again.

Your compact Princess version of Alstroemeria was the product of 'meticulous work focusing on smaller size and an abundance of flowers' by Van Zanten Plants B.V., which holds the trademark name.  Care and feeding are detailed at the Easy to Grow Bulbs.com website:

www.easytogrowbulbs.com/index.asp?PageAction=VIEWCATS&Category=198

They like a Soil pH on the Acid side, 6.0 to 6.5, and full Sun.  Although these plants like warmth, growers are instructed to set the initial temperature to 63 degrees for the first month to encourage strong roots, then drop it to 57 degrees F to produce buds on sturdy, compact growth.  Daylight length must be at least 11 hours long for this plant to bloom.  Remember that if you plan to keep your plants flowering through Winter.

THE LONG ISLAND GARDENER