Is this the relation R:={(2,1),(3,1),(5,5),(7,5)} a function?

This is a function because there are no x values that repeat.

If we had repeated x values, then this would mean a certain input x leads to multiple outputs y, and that would not make it a function.

For instance, if we had (2,1) and (2,2) at the same time, then the input x = 2 leads to multiple outputs y = 1 and y = 2 at the same time. A function would not be possible in this example.

A function is only possible if any input x leads to exactly one output y. It is possible for y to repeat itself and still have a function.