New dates for the Ramayana?

Pondering over a news item:
Rama was born on 10 January 5114 BCE.
Hanuman met Sita in the Ashok Vatika on 12 September 5076 BCE.
The Mahabharata war started on 13 September 3139 BCE.
This is what 'The Institute of Scientific Research' says. Similar dates have been provided earlier, but how does it co-relate with archaeology?
After intensive research on the Vedas, using all available sources I found the earliest possible date for the Rig Veda would be 4000 BCE, and of course it could be later.
No single source is sufficient for trying to establish an approximate date.