Is a 15 foot tall pergola not feasible?
First big question....Are you planning the floor in the pergola at the level of the deck floor? 

Next...


For posts 15 feet vertical height I do not believe that 5 feet depth in the ground is enough. You should vie for a depth of 6 or 7 feet deep.
For a structure like this you want the bottoms of the posts anchored well below the frost depth.
For the type of height that you are talking about it will be absolutely necessary to have some type of angle bracing that will help to keep the structure from racking and parallelogramming.
If you have a floor at deck height this can offer some alternatives where you can place some of the angle bracing below.
It the pergola is meant to provide some shade at the grass level from a top that is 15 plus feet off the ground it will be far less effective than if the shade top were more like 8 to 9 feet overhead.


To add bracing under the elevated pergola floor: