1. Use the half-life concept

   The half-life is the time in which the amount of substance becomes half of its previous value.

   Given:

   • Half-life $= 5$ years
   • Initial amount $N_0 = 64$ g
   • Total time $t = 15$ years

2. Find number of half-lives elapsed

   $n = \frac{t}{t_{1/2}} = \frac{15}{5} = 3$

   So, in $15$ years, the substance undergoes $3$ half-lives.

3. Apply repeated halving

   After 1 half-life: $64 \to 32 \text{ g}$

   After 2 half-lives: $32 \to 16 \text{ g}$

   After 3 half-lives: $16 \to 8 \text{ g}$

   Therefore, amount left after $15$ years is $8 \text{ g}$

4. Using formula check

   $N = N_0\left(\frac{1}{2}\right)^n = 64\left(\frac{1}{2}\right)^3 = 64 \cdot \frac{1}{8} = 8 \text{ g}$

5. Evaluate options

   • A: $16$ g — incorrect
   • B: $2$ g — incorrect
   • C: $32$ g — incorrect
   • D: $8$ g — correct

Hence, the correct answer is Option D.