A faint instagram-shaped beige overlay, always I got a Galaxy S5 (second hand you may note,  however it's in great condition) very recently.
I've noticed that there is a very faint beige-yellow tint on the screen at all times in the shape of the main features of the instagram app.
It's far more obvious on a white background.
Does anybody know why this has happened?
From what you described, it's very likely that your S5 is the victim of screen burn-in. The previous owner likely used Instagram a lot, which burnt the main interface into the screen. The damage is done to the AMOLED screen itself instead of software-based, and thus can't be reverted, unless you decide to replace the screen altogether.