Solve the Prime Factor Equation: What Number Multiplies 5, 13, 11, and 7?

To determine the number with the prime factors $5$, $13$, $11$, and $7$, follow these steps:

• Step 1: Multiply the first two prime factors: $5 \times 13 = 65$.
• Step 2: Multiply the result by the next prime factor: $65 \times 11 = 715$.
• Step 3: Multiply the intermediate product by the last prime factor: $715 \times 7 = 5005$.

Each multiplication step ensures we have correctly included all prime factors to find the original number.

Thus, the number whose prime factors are $5$, $13$, $11$, and $7$ is $5005$.

Referring to the provided multiple-choice options, the correct answer is choice 2: $5005$.