To simplify the expression \( 7^5 \times 7^2 \) using the product rule of exponents, you add the exponents together. The product rule states that \( a^m \times a^n = a^{m+n} \).
So, for your expression:
\[ 7^5 \times 7^2 = 7^{5+2} = 7^7 \]
Therefore, the simplified answer is \( 7^7 \).