Have a look at the right datasheet
http://www.classiccmp.org/rtellason/...ata/bc182l.pdf

Here at 20mA, the minimum you may have should be 80.

-> Why 20mA? Because it is the desired current for the load ?
Yes

To make sure you saturate it properly, some will divide the Hfe parameter by 2, some by 5, and some others by 10.

-> Why? Is this empirical?
good question

Let's use 5, so we have Hfe=16

-> Hm, yes, but why divide it by 5?
I believe dividing by 5 is usually safe enough, while dividing by 10 is much safe... well we drive LEDs, not big current, no big deal.

The base current is the Collector current/Hfe = 20/16 = 1.65 mA

-> This is the current needed at the BASE to saturate and switch the BJT then?
Yes

the base resistor will be
(5-Vbe)/1.65mA = (5-0.7)/1.65mA = 2.606 K...

anything in this range or lower will work.

-> The formulas I found on the web are more complicated and I don't find the same values... ???
What was your result? I use a simple method, proven to work along the years. For switching, there's no real big deal, on/off, that's it. It's an whole different story in, let's say, amplifiers, smal signal etc etc.

Have I said I'm a bad teacher