\[ 5 x^{2}-6 x-8 \] First, choose a form with appropriate signs. Then, fill in the blanks with numbers to be used for grouping. Finally, show the factorization.

Step 1 ：The given expression is a quadratic equation. To factorize it, we need to find two numbers such that their product is equal to the product of the coefficient of \(x^2\) (which is 5) and the constant term (which is -8), and their sum is equal to the coefficient of \(x\) (which is -6).

Step 2 ：Let's denote these two numbers as \(a\) and \(b\). So, we need to solve the following system of equations: \[\begin{align*} a \cdot b &= 5 \cdot -8 = -40, \\ a + b &= -6. \end{align*}\]

Step 3 ：The solution to the system of equations is \(a = -10, b = 4\) and \(a = 4, b = -10\). This means that we can rewrite the middle term of the quadratic equation as \(-10x + 4x\), or \(4x - 10x\).

Step 4 ：Now, we can factor by grouping. The quadratic equation becomes \(5x^2 - 10x + 4x - 8\), which can be rewritten as \(5x(x - 2) + 4(x - 2)\).

Step 5 ：So, the factorization of the given quadratic equation is \((5x + 4)(x - 2)\).

Step 6 ：Final Answer: \(\boxed{(5x + 4)(x - 2)}\)