We have the following:
In this case we must divide the remaining cake into 5 equal parts, which is 1/3 of the original cake, therefore, we must divide:
[tex]\begin{gathered} \frac{1}{3}\div5=\frac{1}{3}\div\frac{5}{1} \\ \text{CrossMultiplication} \\ \frac{1\cdot1}{3\cdot5}=\frac{1}{15} \end{gathered}[/tex]Therefore, each friend of Jamie will have 1/15 of the original cake.