1. The problem asks us to find the value of $r$ in the equation $$\frac{5^6 \times 5^{10}}{5^2} = 5^r.$$\n\n2. We use the laws of exponents: when multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}.$$ When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}.$$\n\n3. Apply the multiplication rule to the numerator: $$5^6 \times 5^{10} = 5^{6+10} = 5^{16}.$$\n\n4. Now apply the division rule: $$\frac{5^{16}}{5^2} = 5^{16-2} = 5^{14}.$$\n\n5. Since the right side is $5^r$, we have $$5^r = 5^{14}.$$\n\n6. Therefore, the exponents must be equal: $$r = 14.$$\n\nFinal answer: $r = 14$.