What does the given function mean?

I am having trouble understanding a question.

A function given as :

Let $f (x+y)=f(x)f(y)$ for all $x$ and $y.$ If $f (5)=2$ and $f'(0)=3$ then $f'(5)$ is equal to what?

So the trouble which I am having is.. Here it is given $f(5) =2$ which would mean $x+y$ is $5.$ Which can be $2+3, 1+4$ & $0+5.$ But none of these on being multiplied as $f(x) f(y)$ give $2.$

Or if I think this way: $f(x)f(y)$ is $2.$ And I get the quadratic equation $x (5-x)^2=2.$ I get an irrational number.

I am sorry if the basic way I thought about it is absolutely wrong. I think I am thinking about it in a wrong way. So I need help understanding the given function first then.

1 Answer

Hint. Differentiate the function $g(x) = f(5 + x)$ at $x = 0$ in two different ways.

Edit. As Abstraction points out in a comment, no function $f$ satisfying the hypotheses can actually exist.