First, there's no need to wait to plant the tank. The plants will help make the water 'right'. They will use the bad stuff like any nitrItes and ammonia.
Did you test tank and tap? Don't you have a more accurate reading than 'between 5 and 6?
What I'd like you to do is take a sample of tap water and set it on the kitchen counter for a few hours. Then test it for pH, gH, kH, phosphates and nitrAtes if you have those kits. Test both tank and tap with whatever kits are available to you and post both sets of results back here. Then we will have a better idea of what you've got and what the tap is giving you. Telling us it's soft doesn't help.....soft is good, but how soft is it?
Also, size of tank, wattage and type of light over the tank, type of substrate filtration. Those kinds of things help in making suggestions.
Len