If you are thinking about expense, yes, buying set weights are useless. Assuming you actually use it, eventually you will be too strong to get any benefits out of that specific weight and will need to resort to buying another one later on.
If you buy bar bells however, with variable weights, that may last you quite a while longer depending on what it is you intend to do with it.
No, your sister is incorrect, unless 5 pounds is actually difficult for you to do lets say a bicep curl, you will not "build" muscle (I assume you mean build by getting larger in mass) because you need to cause considerable stress to your muscles to promote growth.