I wouldn't say that it's an upgrade. They just sound different. Production wise, the BH2 is out to replace the BH1, which was replacing the MK2. The MK2, as well as BH1 and BH2, were collaboration results of Bill Bartolini and top Ibanez engineers, thus they are proprietary to Ibanez basses. OTOH, the MK1 isn't Ibanez specific. They are being used also in Cort, Lakland, and other brand basses.
The different sound is the result of different coil configurations inside. The MK1 has split coil reverse P configuration whereas the BH2 has dual full blade coil configuration. Thus the BH2 sounds thicker, just as typical dual coil humbucker pickups.
But since you were asking for the 5 string configuration, the MK1-5 and BH2-5 have somewhat nearly identical dimensions. So, in case you do buy the SR875 and turns out you don't like the BH2 sound, you can purchase a used pair of MK1-5 (be careful not to be mixed up with MK1-4 and MK1-6 cause the magnet alignment inside are different) which often can be found quite cheap.
Or, you can go all the way up to USA made Bartolini MK5, but this has another different kind of sound than any of the above.