Your engine will be fine. 5-6k miles (8 - 9,000km) is usually no problem for these modern conventionals. With a lot of highway miles (easier on oil/mile driven) in that oil change, one can run much farther than that without issue. You may have pushed the oil a little but modern conventional 5w30 (Group II+) motor oils are much better than those we were using 15 years ago. They use almost synthetic quality base oils.
The Castrol GTX you are using is a good oil, this UOA was 5,049 miles and the TBN was 4.1, which means the oil had lots of life left in it.
Changing oil at 5,000km (3k miles) is a waste with modern conventionals, they go much further than that easily. Run 8,000km (5k miles), and if it mostly highway you can go further.
The Castrol GTX you are using is a good oil, this UOA was 5,049 miles and the TBN was 4.1, which means the oil had lots of life left in it.
Changing oil at 5,000km (3k miles) is a waste with modern conventionals, they go much further than that easily. Run 8,000km (5k miles), and if it mostly highway you can go further.