Its called multiplexing ...
the lights are not actually all on at once, it just looks like that because the flash so fast
You could do 75 in 3 blocks of 25 in 5X5 configuration, obviously that is just one option.
it go's like this ...
Enable block 1, scan through the columns 1 at a time and control LED's with the rows.
Then disable block 1
Thats 5 scans,
Now do the same for blocks 2 and then 3.
Other options
There are display chips specifically designed to do this for huge displays, many are addressed, controlled over a network.
I am no expert but if you start looking at these concepts you will find the info you need.
keywords, multyplex, matrix controller.
If you want specifics look for lighting display controllers they use a protocol called DMX