Safe way connect a 3.3V output to an input with weak pullup to 5V
If you invert logic on the Beaglebone Black software control for the output, then a simple transistor will work.







simulate this circuit &ndash; Schematic created using CircuitLab

(Not sure if the 25kΩ resistor is internal or external to the 5V IC you are using, you didn't name it. If it's internal you don't need to include it.)

When the BBB GPIO is logic HIGH, the 5V input is logic LOW. The transistor is any common small signal transistor, R2's value is not particularly important (1kΩ - 30kΩ), and it needs a ground common to both the BBB and the 5V IC to work.