The amplitude of $\displaystyle{y}={a}{\cos{{b}}}{x}\usepackage{cmbright}\Huge\$ is given by $\displaystyle{\left|{a}\right|}\usepackage{cmbright}\Huge\$ , so the amplitude of $\displaystyle{y}={5}{\cos{{\left(\frac{{x}}{{4}}\right)}}}\usepackage{cmbright}\Huge\$ is 5. The period equals $\displaystyle\frac{{{2}\pi}}{{\left|{b}\right|}}\usepackage{cmbright}\Huge\$ . Now $\displaystyle{5}{\cos{{\left(\frac{{x}}{{4}}\right)}}}={5}{\cos{{\left(\frac{{1}}{{4}}{x}\right)}}}\usepackage{cmbright}\Huge\$ , so $\displaystyle{b}=\frac{{1}}{{4}}\usepackage{cmbright}\Huge\$ and the period equals:

$\displaystyle\frac{{{2}\pi}}{{\left|\frac{{1}}{{4}}\right|}}=\frac{{{2}\pi}}{{\frac{{1}}{{4}}}}=\frac{{{2}\pi}}{{1}}\cdot\frac{{4}}{{1}}={8}\pi\usepackage{cmbright}\Huge\$