What is the greatest resistance that can be created with five $\frac{1}{6}\Omega$ resistors each?

To get maximum resistance, the resistance should be connected in series.

Due to the circuit's current flowing sequentially through each resistor as it is linked in series, the total resistance is equal to the sum of the individual resistances.

The maximum resistance which can be made using five resistors each of $\frac{1}{6}\Omega$ .

Using series resistance formula i.e.,

$R_{eq}=R_1+R_2+R_3+......$

The total resistance when five resistors are linked in series is 

$R_{eq}= \frac{1}{6}+ \frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}= \frac{5}{6}\Omega$.

Hence the maximum resistance is $\frac{5}{6}\Omega$.