How many 5 metre strips of 5050 LED lighting will a 6 amp driver feed without overheating?
One.  

Presuming you're dealing with 12 V and a 300 light strip.

A not entirely universal rule of thumb is 150 lights per amp for 3528's and 50 per amp for 5050s.  That is because 5050s have three emitters per light and each of the three draw about as much as a whole 3528.  If you're using 24V strips, double the number of lights per amp.  Of course, check your data sheets and/or put it on a power supply and test it.