Chapter 4 - Exponential Functions - 4.3 Graphs of Exponential Functions - Exercises and Problems for Section 4.3 - Exercises and Problems - Page 162: 34

See the graph below.

As $x \rightarrow \infty$, we know that $3(0.9)^x \rightarrow 0$ because it exponentially decays to zero. Therefore, as $x \rightarrow \infty$, we have $f(x)= 5+3(0.9)^x \rightarrow 5+0=5$. This function has a horizontal asymptote at 5.