It is because mM is a concentration - if you write it out in full it is written as "millimoles per litre" this does not change based on volume; the concentration is constant. When you are looking at things like this, it is important to make sure that what you are looking at is correct in terms of units. For instance in the sentence:
so the concentration is 5mM in 1L and it means it will be 5nm/ul, but the calculator shows its 5mM in 1ul??
You switch from concentration (mM) to amount (nm) - these are not equivalent mM is a concentration, always indicating amount per litre, and nm is an amount (nanomoles)
The question you are wanting to ask is "how many moles in 1 ul?" In which case you are correct, there should be about 5 nmole in 1 ul.