Old system vs Big HDD

Hi,
simple question.
not looking for philosophy, morality or economy.

if i fit a large HDD into an old computer that only reads xx-gigabytes,

will i encounter any problems?

the system only requires say 5-gigs-hdd so if i fit a 60-gig without using any Bios update or disk management will data be safe?

my reasons are unimportant but please treat me as knowing the answer to everything except this question.

??)

thanks