Is Boeing coming out with a B767-500 aircraft anytime in the future?

No need to, thanks to the 787.

No, because the 787 Dreamliner is as big as the 767.

No need to, thanks to the 787.

No.  The basic design is over 40 years old.  The 787 now targets the 767 niche but with better fuel economy and longer range.  Boeing delivered the last passenger 767 in 2013.

The only reason the 767 assembly line is still alive is to build the KC-46 tankers for the Air Force, plus the six remaining 767-300Fs for FedEx and one for UPS.

Why on Earth would they?

The 767 largest variant, the 400, typically seats 296 passengers in two classes; that is what the 787-9 offers. Boeing has trouble competing with Airbus, why would they compete with themselves on top of it?

If they had any plans to do so, then they’ll be on ice.

With very little worldwide demand for passenger air travel and with immensely reduced demand for air freight services, launching any new airliner variant is simply too large a gamble.

Boeing are already hanging by a thread over the 737-MAX relaunch which is already doing disastrously.

It’s not just Boeing: Mitsubishi has a design mothballed for a small passenger airliner which was fully ready to go into production early last year: 2020 has probably killed that as by the time that airline demand has risen sufficiently the cutting-edge modern design will no longer be particularly advanced.