1. Stating the problem: Simplify the series $5 - 10 + 15 - 20 + 25 - 30 + \ldots + 95 - 100$. 2. Notice the pattern: the terms alternate between adding and subtracting multiples of 5, starting from 5 and ending at 100. 3. Group terms in pairs: $(5 - 10) + (15 - 20) + (25 - 30) + \ldots + (95 - 100)$. 4. Each pair simplifies as follows: $5 - 10 = -5$, $15 - 20 = -5$, $25 - 30 = -5$, and so on. 5. Count the number of pairs: terms go from 5 to 100 in steps of 5, so there are $\frac{100}{5} = 20$ terms. 6. Since terms are paired two at a time, the number of pairs is $\frac{20}{2} = 10$ pairs. 7. Each pair sums to $-5$, so total sum is $10 \times (-5) = -50$. 8. Final answer: The sum of the series is $$-50$$.