Just re-read and it says:
"A total of 1,000 Asia Miles will be given in each single transaction. Splitting of transaction will not be accepted. *Each Asia Miles member can earn up to 5,000 Asia Miles per day."
That seems to imply that you must go to the check out a total of 5 times (each with 500HKD min spend) to get the 5K miles per day.
Illogical!