from what i read and understood (if i understood anything) i have this theory

you want a keyboard of 2 buttons and push them 1600 times? try the matrix keypad (4x4)

5*8bits = 40 bits, you make this 40 times. 5*8*40 =1600 bits

you can take a keypad of 4x4, and enter 5 keys (your first string of 40) and then press enter and do it 40 times

ok, you have 40 strings of 5 bytes coming,
do you need to have al least 200 bytes of RAM. i'm curious what are you going to do with 200 bytes of DATA??? i wouldn't what to do with that much information