There were different capacities of battery available for these cars when new, so a Leaf with the small battery could well have a range of 80 miles - my brother's has the big battery which gives a reliable 130 miles range & still does with the car nearly 4 years old (he bought an ex-demo car). It might be worth checking who owns the battery, as I seem to think that as well as the two battery capacities, there were options to lease the batteries as well as buy them outright. There were different capacity chargers supplied as well, so it pays to research the model thoroughly to make sure you know what you are looking at.
IIRC the batteries have a 7 year warranty & they are changed if capacity gets less than 75%, so a 5 year old car with a sub-standard battery should have it changed by Nissan FOC under warranty. Part of the annual service is a check on battery capacity & performance.