d) \( \lim _{x \rightarrow \infty} \frac{e^{5 x}}{3 e^{3 x}+5} \)

To evaluate the limit \( \lim _{x \rightarrow \infty} \frac{e^{5 x}}{3 e^{3 x}+5} \), we can simplify the expression by dividing both the numerator and the denominator by \( e^{3x} \): \[ = \lim _{x \rightarrow \infty} \frac{e^{5x}}{3 e^{3x}+5} = \lim _{x \rightarrow \infty} \frac{e^{5x}/e^{3x}}{3 + 5/e^{3x}} = \lim _{x \rightarrow \infty} \frac{e^{2x}}{3 + 5/e^{3x}}. \] As \( x \) approaches infinity, \( e^{3x} \) grows rapidly and thus \( 5/e^{3x} \) approaches \( 0 \). Therefore, we have: \[ = \lim _{x \rightarrow \infty} \frac{e^{2x}}{3} = \infty. \] Thus, the limit is \( \infty \).