Answer
$(x-1)(5x+3)$
Work Step by Step
Step 1: There is no common factor in the term $5x^{2}-2x-3$.
Step 2: However, this expression can be factorized further by grouping:
$5x^{2}-5x+3x-3$.
Step 3: $5x(x-1)+3(x-1)$
Step 4: $(x-1)(5x+3)$
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