uL = microliters. Different fields (or even people) talk about concentrations in different ways, and mg/mL is not uncommon.
Also, no, taking a small amount out does not increase the concentration unless you're evaporating the solvent. Otherwise the ratio of solute/solvent is exactly the same. Evaporating the solvent increases the concentration, diluting it in solvent decreases the concentration.
With regard to the original question, the first dilution is the key, and you didn't specify how much you started with. If you started with 60 uL of a 5 mg/mL solution and then took 30 uL to dilute with 30 uL of EtOH, THEN you're cutting the concentration in half. However, if you have 1 mL of a 5 mg/mL solution and take 30 uL, you're getting 1.5 mg out rather than 2.5. But your formula for the remaining dilutions is correct.