To approximate $5^{1.7}$ to three decimal places:

1. Calculate $5^{1.7}$ using a calculator.
2. The result is approximately $14.696$.

So,

$5^{1.7} \approx 14.696$

Let me know if you would like more details or have questions.

Here are some related questions:

1. How would you approximate other non-integer exponents, like $7^{2.5}$?
2. Can you calculate the approximate value of $6^{1.3}$ to three decimal places?
3. What are the general rules for exponentiation with non-integer exponents?
4. How does this type of exponentiation relate to logarithmic calculations?
5. Why is rounding necessary in approximation, and what impact does it have on accuracy?

Tip: When working with exponents, using a calculator’s power function can help ensure accuracy, especially with non-integer exponents.