You'll have to take steps to scale the voltage down to the BBB's 3.3 V I/O level. The best way to do this is with dedicated voltage-level translator ICs. But depending on your application, you might be able to get away with current-limiting resistors in series from the 74xx output to the GPIO (you'll have to do some work to find the right value), and with the right 74xx selection, you won't need to put anything between BBB outputs and 74xx inputs (that will depend on what the 74xx Vhi threshold is).
It's reasonable to do that when you have a 5 volt system with a number
of lines, and can't substitute the part (a 5 volt display, for
I would NOT use current limiting resistors, I don't thing that they
solve the problem.
As I remember it, and they could have changed things and this is not
as much of a problem now, the way that the pin is internally
constructed involves back biased diodes which connect to the power
supply rails. These back biased diodes, if forward biased, make an
SCR, which once turned on, stays on until the power is interrupted.
The voltage causes these SCR's to become functional, then fire. The
SCR then uses the internal power supply to provide enough energy to
destroy the I/O structure in the chip.
Current limiting resistors do not help, because it's not the current
coming in that does the damage, it's the relative voltage level.
This is called a "parasitic SCR" and has destroyed chips in the past.
Whether or not it is a problem still, I do not know.
You'd want to have chips (to connect the 5 volts to) that have 5 volt
tolerant inputs. These processors do not.
Better to use 3.3 volt logic everywhere possible, and level translate
only when talking to a 5 volt system that cannot be redesigned.
Talking, in this case, means signals going either direction.
Or maybe you can use 3.3 V 74xx variants.
This would be my preferred solution, yes.