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Given that the total length of the ribbon on the roll is 5 yards.
Janet cuts 1 (1/3) yards of ribbon from the roll, then the remaining length of ribbon on the roll is calculated as,
[tex]\begin{gathered} \text{Remaining Ribbon length=Total Length-Length cut out} \\ \text{Remaining Ribbon length=}5\text{ yards-1}\frac{1}{3}\text{ yards} \\ \text{Remaining Ribbon length=}(5-\frac{4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{15-4}{3})\text{ yards} \\ \text{Remaining Ribbon length=(}\frac{11}{3})\text{ yards} \\ \text{Remaining Ribbon length=3}\frac{2}{3}\text{ yards} \end{gathered}[/tex]Thus, the length of the ribbon left on the roll is 3 (2/3) yards.
So the second option is the correct choice.