Answer:
see the attachment
Explanation:
You want graphs of f(x -5) and f(x)+2 and their asymptotes, given exponential function f(x).
f(x-5)
The subtraction of 5 from the argument x causes the graph to be shifted to the right 5 units. The horizontal asymptote at y=0 is unchanged.
f(x)+2
The addition of 2 to every function value causes the graph to be shifted up 2 units. The horizontal asymptote is likewise shifted up 2 units to y=2.
The red and blue graphs are attached. The asymptotes are dashed lines.