BoFIV was really the downfall of the series, and V was just the nail in the coffin. It was typical crap where Capcom thinks people lost interest in the series, but really they just lost touch with the series. BoFII Nina is a quiet, serene and graceful woman, whereas BoFV Nina is a whiney little kid that won't ever shut up.
One of the recurring characters in the series returns as a tin-bodied robot in BoFIV for no reason at all, and it seems like they completely forgot to develop character background. All of the charm was gone. So, I recommend playing I-III, and then only playing IV and V to see what made it all fall apart.