1. **State the problem:** Simplify the expression $\frac{5x^2}{5x}$.\n\n2. **Recall the rule:** When dividing powers with the same base, subtract the exponents: $\frac{a^m}{a^n} = a^{m-n}$. Also, common factors in numerator and denominator can be canceled.\n\n3. **Apply the rule to the coefficients:** $\frac{5}{5} = \cancel{5}/\cancel{5} = 1$.\n\n4. **Apply the rule to the variable:** $\frac{x^2}{x} = x^{2-1} = x^1 = x$.\n\n5. **Combine the results:** $1 \times x = x$.\n\n**Final answer:** $x$