You are trying to measure a difference in weight of 5 mg between an empty vial and the same vial containing 5 ul of water, on a balance that reads to 1 mg.
So you have only 5 increments of measurement result.
To demonstrate a 1% repeatability of the pipette you need better than 1% repeatability in the weighing - this will need a 5 figure balance if you are weighing 5 ul of water.
To see for yourself, determine the repeatability of the weighings - tare the balance, weigh the empty vial, tare again, re-weigh and repeat for 5 replicates. What is the standard deviation. Add 5 ul of water and repeat for 5 replicates. What is the standard deviation. What are the standard deviations as a fraction of 5 mg ?
Also, check the specifications of the balance for its minimum weight.
Peter