Does the SIM Card for an iPhone 7 will work on an iPhone 5?

From the physical point of view, the answer is yes, as both devices accept only nano SIMs.

As far as their compatibility is concerned, it depends on the carrier (current or future) and / or on the carrier's software update, keeping in mind that iPhone 5 can't support iOS versions beyond 10.3.4.

Regards

Giulio

It should. If the 5 was locked to a carrier, then the SIM card must be from that same carrier.

~Lyssa