1. The problem is to simplify the expression $5x - 5x$. 2. The formula used here is the distributive property and combining like terms: $a x - a x = (a - a) x = 0 \cdot x = 0$. 3. Applying this to the expression: $$5x - 5x = (5 - 5)x = 0 \cdot x = 0$$ 4. Since $5x$ and $-5x$ are like terms with opposite coefficients, they cancel each other out. 5. Therefore, the simplified expression is $0$.