1. The problem asks for the function whose graph is the same as $y=\frac{1}{x}$ shifted right by 5 units and up by 2 units. 2. The original function is $y=\frac{1}{x}$, a hyperbola. 3. Horizontal shifts are done by replacing $x$ with $x - h$ where $h$ is the number of units shifted right. So shifting right 5 units means replacing $x$ with $x - 5$. 4. Vertical shifts are done by adding or subtracting a constant outside the function. Shifting up 2 units means adding 2 to the function. 5. Applying these shifts, the new function is: $$y = \frac{1}{x - 5} + 2$$ 6. Therefore, the correct function is $y=\frac{1}{x-5}+2$.