Step 1: Define variables for the ages

Let the son's age be $S$. According to the problem, the mother's age is three times the son's age, so Mother = $3S$. The daughter is 5 years older than her brother, so Daughter = $S + 5$.

$M = 3S, \quad D = S + 5$

Step 2: Set up the sum equation

The sum of the ages of the mother, son, and daughter is given as $70$ years. Substituting our expressions into the sum: $S + 3S + (S + 5) = 70$.

$S + 3S + (S + 5) = 70$

Step 3: Solve for the son's age $S$

Combine like terms: $5S + 5 = 70$. Subtract $5$ from both sides to get $5S = 65$, which gives $S = 13$.

$5S = 65 \implies S = 13$

Step 4: Calculate the mother's age

Since the mother's age is $3S$, substitute $S = 13$ into $3S$: Mother's Age = $3 \times 13 = 39$ years.

$3 \times 13 = 39 \text{ years}$