5) \( (a+b)^{2}+4(a+b)-32 \)

To tackle the expression \( (a+b)^{2}+4(a+b)-32 \), let's simplify it. Let \( x = a + b \). Thus, the expression transforms into \( x^2 + 4x - 32 \). This is a quadratic equation which we can factor or use the quadratic formula to solve. To factor it, we look for two numbers that multiply to \(-32\) and add to \(4\). These numbers are \(8\) and \(-4\). So we can factor it as \( (x + 8)(x - 4) = 0 \). Therefore, \( x + 8 = 0 \Rightarrow x = -8 \) and \( x - 4 = 0 \Rightarrow x = 4 \). Substituting back \( x = a + b \), we find that \( a + b = -8 \) or \( a + b = 4 \). This expression highlights how we can easily manipulate algebraic equations through substitution and factorization to arrive at solutions!