Methodology / Template for calculating application reliability five nines / six nines?

For predicted reliability, you multiply the predicted reliability of all critical components together (assuming the reliability is independent, which is generally unsafe). With non-critical components, you have to decide if they come together to form a critical system, or if there is some characteristic time for which they might not be available before critical, or ... Well, in general, you just got analyze very carefully.

But predicted reliability is not the same as measured reliability ! If you are serious about this (and generally 99.9999% reliability is very serious stuff) then you have to measure and you have to work out very carefully what needs to be measured and from what point of view. There is no point in measuring website availability within the same cluster if off-site network bandwidth is a common deployment issue.