How long will iPhone 5s last?

I do not mean battery life. I have 2 years contract so will the phone still be quick without much lag

Tech wise: Up to 2 or 3 years
Material wise: Really good care - up to 8 years
Latest and greatest wise: 1 or 2 years

I find the issue of lengthy contracts bothersome

I don't believe any phone with "normal people" usage can survive 2 years

I have sidestepped the issue by only buying used phones at reduced prices

when it develops problems, cracks, is lost, takes a dive in the toilet, I just buy another one

Yes. That mostly comes down to iOS & its optimizations but Apple is usually on top of that. I had an iPhone 4 for 2 years, no complaints, I have an iPhone 5 coming up to 2 years, again no complaints.