$R_5 \leq \int_5^{\infty} \frac{1}{x^3} dx = \frac{1}{50}$

$R_5 \leq \int_6^{\infty} \frac{1}{x^3} dx = \frac{1}{72}$

$R_5 \geq \int_6^{\infty} \frac{1}{x^3} dx = \frac{1}{72}$

The remainder cannot be bounded by an integral