Let's plug in x = 2.
f(x) = x^2
f(2) = 2^2 ... replace every x with 2
f(2) = 4
----------
Now plug in x = 3.
f(x) = x^2
f(3) = 3^2 ... replace every x with 3
f(3) = 9
-----------
And x = 5 as well.
f(x) = x^2
f(5) = 5^2 .... replace every x with 5
f(5) = 25
-----------
We see that
f(2)+f(3) = 4+9 = 13
which is not equal to f(5) = 25.
So f(2)+f(3) = f(5) is false.
------------
Another way to phrase why it doesn't work is because (2,3,5) isn't a pythagorean triple. The equation 2^2+3^2 = 5^2 is false.
If it said f(3)+f(4) = f(5), then it would be correct because 3^2+4^2 = 5^2 is a true equation.