Actually Looking at the reports from the first test, the splash down was “somewhere” along the southern tip of Africa and Australia.
Southern Tip of Africa is 35° S and Australia is 44°S and Wheeler islands is at 20°N.
To a latitude range near South Africa the total distance traveled is 55° of latitude. I remember learning in geography that every degree of latitude covers 111 kilometers. This would make the distance traveled at about 6100 kms. If we consider the latitude range of southern Australia, total distance traveled is 64°. which puts total distance traveled at 7100 kms. A median of this is 6,600 kms.
Also consider that the DRDO has said that the flight time is about 20 minutes at speeds of about 25,000 kms per hour. Doing the math, it works out to 8,300 kms. Yes it does take some time to reach that speed but still means a total travel of about 8000 kms.
The missile was tested in a depressed trajectory which is not quite an ideal way and is a non-optimal, lower and flatter trajectory which takes less time between launch and impact.
Soon after the first test, the Chinese officially said that they think the range of India’s Agni V is 8000 kms. We have heard about China having monitoring station on Coco Islands as well as monitoring by satellites and sea based radars on their naval assets.