Four Liters From 3 and 5

First make $2$ liters in the big jug.

Then the small jug has room for exactly $1$ more liter.

1. 1. Make 2

   Fill the $5$, pour into the $3$: $2$ liters remain in the $5$.

2. 2. Store it

   Empty the $3$ and pour the $2$ liters into it.

3. 3. Finish

   Refill the $5$ and pour into the $3$ until full ($1$ liter). The $5$-liter jug now holds $4$ liters.

4. 4. Key idea

   Any amount $ax+by$ with $\gcd (3,5)=1$ is reachable; work backwards from the target.

Answer: Fill 5, pour into 3 (2 left), empty 3, pour the 2 in, refill 5, top up 3 with 1: 4 liters remain in the 5