No, the DJI Osmo Action 5 Pro is not compatible with the Lexar Professional CFexpress Type A Gold 256GB.
DJI Osmo Action 5 Pro has a microSD-only card slot (no CFexpress support of any type). Its own product page confirms only microSD card compatibility -- CFexpress Type A uses a physically different, much larger connector and cannot be inserted into a microSD slot.
What works instead
See all compatible camera for the DJI Osmo Action 5 Pro →“Supported SD Cards microSD (up to 1 TB) Recommended microSD Cards”
Last verified:
Compatibility inferred from spec rule (citations above are manufacturer-verified)