To determine the equation of the asymptote for the function [tex]\( f(x) = \ln x + 5 \)[/tex], we need to consider the properties of the natural logarithm function [tex]\( \ln x \)[/tex].
The natural logarithm function [tex]\( \ln x \)[/tex] is undefined for values of [tex]\( x \le 0 \)[/tex]. This means that the function [tex]\( \ln x \)[/tex] has a vertical asymptote at [tex]\( x = 0 \)[/tex]. This characteristic does not change when we add a constant to the function. Therefore, [tex]\( f(x) = \ln x + 5 \)[/tex] will also have a vertical asymptote at [tex]\( x = 0 \)[/tex].
Hence, the correct answer is:
A. [tex]\( x = 0 \)[/tex]
