Factor by grouping (sometimes called the ac-method).
\[
6 x^{2}-13 x-5
\]

First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for groun Finally, show the factorization.
Form:
\[
\begin{array}{l}
6 x^{2}+\square x+\square x-5 \\
6 x^{2}+\square x-\square x-5 \\
6 x^{2}-\square x+\square x-5 \\
6 x^{2}-\square x-\square x-5
\end{array}
\]

Step 1 ：Find two numbers that multiply to \(6 \times -5 = -30\) and add to -13. These numbers are -15 and 2.

Step 2 ：Rewrite the original expression, splitting the -13x term into -15x and 2x: \(6x^2 - 15x + 2x - 5\).

Step 3 ：Group the terms and factor out the greatest common factor from each group: \(3x(2x - 5) + 1(2x - 5)\).

Step 4 ：Factor out the common factor \((2x - 5)\) to get the factorization: \((2x - 5)(3x + 1)\).

Step 5 ：Check the work by expanding the product to see if we get the original expression: \((2x - 5)(3x + 1) = 6x^2 - 15x + 2x - 5 = 6x^2 - 13x - 5\).

Step 6 ：So, the factorization of \(6x^2 - 13x - 5\) is \(\boxed{(2x - 5)(3x + 1)}\).