Which boards with ARM(like stm32, etc.) can have GPIO pins which can give 3.8V or higher as an output?
How fast do you need the pulses?

There are very few 5V ARM cpus (e.g. The NXP KE series parts @Wouter van Ooijen mentioned). And the dev board for those parts here runs the CPU at 3.3V not 5V.

There may be an arm dev board out there with 5V IO but if there is one you're not going to have much choice on part.

However there are lots of 5V tolerant parts available on boards, if you configure the IO pins as open drain (high impedance for a high output) and connect a pull up resistor to 5V then you can get a 5V output from the part.
The down side in this is that the rising edges aren't particularly sharp, for high speed signals or something with very critical edge timing this may be an issue.

If you need a sharp edge then a 3V3 part and a buffer to drive the line is probably your best option.