5,000 would be way off for 5970. Keep in mind that Patek produces
about 20,000 of all watches per year, and the largest production is the
Twenty-Four quartz watch. After that, there are lots of various
models of Calatravas, less still of the various small complication
models, even fewer of the more common grand complications (perpetual
calendar only). For 5970, the best estimates of production
capability put it at 200 per year (1% of Patek's production), and since
there were about 2 years of production of white gold and rose gold
before they were discontinued, that's about 200 total of each.
Yellow gold will likely be another 200, for a total of 600 5970s, not
the 5000 5970s you mention. For, 3970 the best estimate I've
heard is 2700 total over the 18 year it was produced (100 per year for
the first 9 years, and 200 per year for the last 9 years).
Eric von Schonberg