The graph of $\displaystyle{y}={5}\sqrt{{2}}{\sin{{\left(\frac{{1}}{{8}}{x}\right)}}}\usepackage{cmbright}\Huge\$ does pass through the point $\displaystyle{\left({2}\pi,{5}\right)}\usepackage{cmbright}\Huge\$ . However, its amplitude is $\displaystyle{5}\sqrt{{2}}\usepackage{cmbright}\Huge\$ , while the function that was graphed has an amplitude of 5. Also, the period of this function is $\displaystyle\frac{{{2}\pi}}{{\frac{{1}}{{8}}}}={16}\pi\usepackage{cmbright}\Huge\$ , while the function that was graphed has a period of $\displaystyle{8}\pi\usepackage{cmbright}\Huge\$ . The correct answer is $\displaystyle{y}={5}{\sin{{\left(\frac{{1}}{{4}}{x}\right)}}}\usepackage{cmbright}\Huge\$ .