What motherboard ID is appropriate for MKS BASE V1.5 in Marlin Firmware?
Marlin appears to support older versions of the board (and possibly this one) according to this line 

#define BOARD_MKS_13            47   // MKS v1.3 or 1.4 (maybe higher)


in boards.h which can be found here.  

The company also has a guide and looks to provide pre-configured (but not fully configured?) downloads of Marlin.  They have different links for different displays but then ask you to change lines manually but don't mention changing the board so I have no idea what they are doing or what is different between the downloads.

It appears either way you go (Marlin from Github or from Osoyoo) you will need to change some lines to get each axis to behave correctly.