It appears to be 2.54mm (or possibly 2.50) pitch, which are common pin spacings.
But, from the photo, it's not clear what the mating connector pins or cable end fit in to..
That looks more like the back rather than the connecting face?
I thought FPC at first but it looks a bit chunky for that. I'm with the PCB suggestion but it might be thinner than Veroboard.
You converting a hand held device into a free-standing device, Billo? It looks suspiciously similar to the inside of a DMM...