Change the oil every 15,000 km?

Don't see a year or what the mileage is on the odometer; probably doesn't matter. Engine lubricants, synthetic or petroleum based oils will also have a spec referring to "...or whichever comes first". In other words, the 15,000 kms. would likely be something like 6 months - which would be the case for a quality synthetic. Another factor is the driving conditions, ie. normal or severe? I use quality synthetic that protects the engine for up to 16,000 kms or 6 months- whichever comes first but have driven it longer.

Yes fine, change the filter too

You need to change regular motor oil every 3,000 miles or tarnish builds up in the motor and if you have adjustable cam timing the actuator will fail.
I'll let you do the conversions.

Modern engines with modern oil and filters can go 15,000 km between oil changes unless you drive mostly short trips. In that case change it every 7,500 km.

That's about right. 5000km (3000mi) is too soon unless you've been really hard on the car, though the garages would love to see you that often. 10-15000km is fine, and some manufacturers are actually recommending longer intervals than that with the synthetic oils.

How many km do you have on car now? Might mean your next change will be when your odometer reads 15,000 km.

There is nothing to stop you changing this oil earlier. Also, in the UK fully synthetic oil is changed at about 12,000 miles. That's factual.

15,000 km (9,000 miles) seems long to me, unless you take long highway trips, exclusively.

5000 km would be better if you take lots of short trips. Stretch it to 10,000 km if your driving habits include longer trips a few times a week; 40 km or longer.

I'm not aware of any non-synthetic that's rated for 15,000km. Read this post on what goes into determining oil change intervals

http://ricksfreeautorepairadvice.com/when-to-change-oil/