You can indeed move the SD Card from a Galaxy S5 to a Galaxy S10e, Hoodad. Before you do, be sure to check that the SD card is not encrypted. An encrypted SD card can only be used in the device it is paired to.
Yes. I unmounted the card on the s5 and placed it in the s10e. Once I transferred all other data (contacts, texts apps, etc), the photos were eventually displayed. There is a delay on the process so be patient. To get game data to the new phone just login to facebook on the old phone, then on the new phone. Hope this helps.