1. The problem states: "The product of 5 and the sum of -6 and a number is -20." We need to write this as an equation using $x$ to represent "a number."\n\n2. The phrase "the sum of -6 and a number" translates to $(-6 + x)$.\n\n3. The phrase "the product of 5 and the sum" means multiply 5 by the sum, so we write $5 \times (-6 + x)$.\n\n4. The phrase "is -20" means equals -20, so the equation is: $$5 \times (-6 + x) = -20$$\n\n5. We do not simplify as per the instruction, so the final equation is: $$5(-6 + x) = -20$$