New quartz analogue watch losing 5 minutes a day.

How to change date on a watch?
Pull out the crown to the second click, and advance the hour and minute hands until the desired date and day appears. * If your watch has three hands, pull out the crown when the second hand is pointing to 12 o'clock. 5. Adjust the time by turning the crown in the desired direction.

Instructions for Analogue Quartz and Mechanical Watches - Seiko

https://www.seikowatches.com/support/ib/pdf/Analogue_E.pdf Search for: How to change date on a watch?
How to set new date of month on watch Google Search

Yes. The minute hand ticking every 10 seconds is normal. Losing time is either battery or a movement malfunction. Only a trained watchmaker (or presumably Omega) can determine which. Take it back to Omega

Interesting question. I know little about watches but, as you would know, your watch does have a quartz movement, so, from Wikipedia, 'Quartz clock':

Standard-quality resonators of this type are warranted to have a long-term accuracy of about 6 parts per million at 31 degrees C (87.8 F): that is, a typical quartz wristwatch will gain or lose 15 seconds per 30 days (within a normal temperature range of 5 deg C / 41 F to 35 deg C / 95 F) or less than a half second clock drift per day when worn near the body.

If a quartz wristwatch is "rated" by measuring its timekeeping characteristics against an atomic clock's time broadcast, to determine how much time the watch gains or loses per day, and adjustments are made to the circuitry to "regulate" the timekeeping, then the corrected time will easily be accurate within 10 seconds per year. This is more than adequate to perform celestial navigation.

Assuming that you have a computer with internet-synced time and good internet, meaning around 1/100 second accuracy, why not compare the watch to the computer over the space of a week?

No unfortunately there is not, the problem is in the timing module where the quartz crystal is. The only option is to have it checked out to see if anything can be done.

No unfortunately there is not! you have gone as far as you can go by changing the battery. The problem lies in the timing module that houses the quartz crystal, it vibrates at a certain frequency that is critical for keeping time. This will require a jeweler who specializes in this type of repair to address the situation.

Hello,
I am not sure if I understand your question. Are you asking how this particular quartz movement operates?

All Quartz movements are pretty much the same operational wise. They can vary greatly in materials used for construction and number of jewels.

At it's basic a quartz watch uses a piece of quartz crystal called a transistor oscillator to vibrate a tuning fork. This vibration is a is brought down by micro processors to a meaningful number then converted into mechanical energy trough the movement and hands.

In the case of a chronograph it means more internal gears and jewels.
Although this is a good movement it is the low side of middle of the road.

The G10.211 is an analog display of hours and measured time. These include hours, minutes and a small jumping second as 6 o'clock. Mechanical date and counters for 1/10 second, 60 seconds and 30 minutes with "ADD" and 'SPLIT" functions. Operated by 2 push buttons.
It has 6 jewels.

If you want to know something more specific please just ask.
Hope this helps.

I believe you are just outside your warranty. Its time to see a watch maker/technician about repairing the watch. Often times slowing is as easy to fix as lubricating the movement and forcing the gear train through the use of a cyclonic device. This fix takes minutes and is very cost effective. If the slowing is due t circuit board issues or a more sever gear train problem then the movement will need to be overhauled. I suggest comparing this cost to the cost of a replacement movement.

yes they do but it is pricy

There is nothing wrong with your watch. Probably it's the one measuring heart rate and pulse (heart beats per second).
Use your users manual to set the watch.
By the way: Timex is one of the worst watch producers.