Simple Signed Adder is complex to understand

I should say that actually all operations (add/subtract/mult/div) are basically similar for signed and unsigned (using two's complement) but some care is needed with carry bits and result width.

But all these details are not relevant to me as the functions in libraries look after it. I will add one bit to result of +/- and for multiplying 5 bits x 5 bits the result should be 10 bits.

The compiler tells you but not always.