Finding Constants in a Polynomial

Consider the polynomial function defined by $$f(x) = 4x^4 - 8x^3 + 2ax^2 + bx + 5$$, where $a$ and $b$ are constants. It is known that the function has a local maximum at $x = 1$ and passes through the point $(0, 5)$. Additionally, the function's local maximum value at $x = 1$ must equal 5. Determine the value of $$a + b$$.