Accuracy of a vintage Rolex 1016

[ventivent]

First off, I'm a Rolex newb. After several years of toiling away at medical school and residency, I finally have some disposable income, and splurged on my dream watch, a circa 1983 Rolex 1016, 1570 movement, hacking.

It was purchased from a watch dealer, who serviced the watch before sending it out to me. It's a great watch, and I have been using it as my daily wearer. I wear it for about 12-15 hours, and then lay it flat, face-up at night. I notice that it gains about 5-6 seconds a day. Is this a reasonable expectation regarding this watch's accuracy, or can/should it be better? Will taking it to a Rolex Authorized Service Center help significantly?

I have read that placing the watch vertically, crown up will help with a watch that runs a few seconds fast/day, and have yet to try that.

Thanks for your help.