Step 1: Identify constants $ a $ , $ b $ and $ c $.
$ a $ is a number in front of the $ x^2 $ term $ b $ is a number in front of the $ x $ term and $ c $ is a constant. In this case:

$$ a = 5 , b = 6 ~ \text{ and } ~ c = -8 $$

Step 2: Multiply the leading coefficient $\color{blue}{ a = 5 }$ by the constant term $\color{blue}{c = -8} $.

$$ a \cdot c = -40 $$

Step 3: Find out two numbers that multiply to $ a \cdot c = -40 $ and add to $ b = 6 $.

Step 4: All pairs of numbers with a product of $ -40 $ are:

PRODUCT = -40
-1     40	1     -40
-2     20	2     -20
-4     10	4     -10
-5     8	5     -8

Step 5: Find out which factor pair sums up to $\color{blue}{ b = 6 }$

PRODUCT = -40 and SUM = 6
-1     40	1     -40
-2     20	2     -20
-4     10	4     -10
-5     8	5     -8

Step 6: Replace middle term $ 6 x $ with $ 10x-4x $:

$$ 5x^{2}+6x-8 = 5x^{2}+10x-4x-8 $$

Step 7: Apply factoring by grouping. Factor $ 5x $ out of the first two terms and $ -4 $ out of the last two terms.

$$ 5x^{2}+10x-4x-8 = 5x\left(x+2\right) -4\left(x+2\right) = \left(5x-4\right) \left(x+2\right) $$

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