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Understanding dilutions

Hello there,

I wonder if anyone might please be able to help me out? I really struggle to understand the concept of dilutions and converting units in chemistry.**

I've been told that ...

If I take 5 mg of chloramphenicol and mix it with 1 ml of ethanol, I will have a solution of 5 mg/ml.
If I was then to take 100 micro litres of this solution and add it to a container of 100 ml of a substance, I will now have a final concentration of 5 micro grams per ml.

I don't understand the maths and dilution concept of how I got from 5 mg/ml to 5 micro grams per ml.*

If anyone could help me out and talk me through this I would be very appreciative.

Many thanks*