The density function is just the piecewise function,
[tex]f_X(x)=\begin{cases}\dfrac1{22-5}=\dfrac1{17}&\text{for }5\le x\le22\\0&\text{otherwise}\end{cases}[/tex]
i.e. a rectangle of height [tex]\dfrac1{17}[/tex] and length 17 plotted over the interval [tex][5,22][/tex]. Any probabilities that you need to find are then areas of smaller rectangles.
