A company produces two products, A and B. The profit from producing product A is given by the quadratic equation $P_A = -2x^2 + 12x - 16$, where $x$ is the number of units of product A produced. The profit from producing product B is given by the quadratic equation $P_B = -y^2 + 8y - 15$, where $y$ is the number of units of product B produced. The company needs to maximize its total profit, but it can only produce a total of 5 units combined of products A and B. What is the maximum profit the company can achieve? Let's think step by step and output the final answer within \boxed{}.
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