The ratio of syrup and water in $30$ litre of a mixture is $1:5$, then the amount of water required to mix to make the ratio $1:6$ is:

Step 1: Calculate initial quantities of syrup and water
* Total mixture volume = $30\text{ litres}$
* Ratio of syrup to water = $1:5$
* Total ratio parts = $1+5=6\text{ parts}$

$$\text{Value of 1 part}=\frac{30}{6}=5\text{ litres}$$

* Initial Syrup = $1\times 5=5\text{ litres}$
* Initial Water = $5\times 5=25\text{ litres}$

Step 2: Find new required amount of water
We are adding only water, so the quantity of syrup remains unchanged at $5\text{ litres}$.
The new target ratio of syrup to water is $1:6$.

In this new ratio, $1\text{ part}$ represents the syrup content ($5\text{ litres}$).

$$\text{Required new volume of water}=6\text{ parts}=6\times 5=30\text{ litres}$$

Step 3: Calculate the water to be added

$$\text{Water to add}=\text{New water volume}-\text{Initial water volume}$$

$$\text{Water to add}=30-25=5\text{ litres}$$