Connecting multiple LED strips in parallel to a 220v/5A power line (via 12V driver)
When I look at the LED specs, it says the power consumption is 72W for 5m which I take means a current draw of 6A.


You say each strip will use 72W so 12V 6A.

Switching 12V DC power supply usually have an efficiency in the 80-90% range, so for a 72W output it will draw between 80W and 90W on 230 VAC, which corresponds to 0.4A max per 72W strip.

That's 2A for five strips, so you can use your 230V 5A outlet, no problem.

You can use a 12V 6A (or more) supply per strip, or a 12V 30A (or more) supply for all strips. 

Note that 72W*5 gives about 28000 lumens, which is enormous.