1. **State the problem:** Simplify the expression $1 - \left(-3\right) - 5$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. So, $a - (-b) = a + b$. 3. **Apply the rule:** $$1 - \left(-3\right) - 5 = 1 + 3 - 5$$ 4. **Perform the addition and subtraction from left to right:** $$1 + 3 = 4$$ 5. **Continue:** $$4 - 5 = -1$$ 6. **Final answer:** $$\boxed{-1}$$