I dont believe the Dalia Lama is authoritative to make such a claim that it will last another 5000 years.
Here is why, I think not:
Once a disciple asked a living Buddha, what will happen to his teachings and the religion if he were to pass away because they will be without a leader. The disciple was worried that the religion will die a natural death without a chrismatic leader.
The Buddha gave him such an answer;
Take a drop of water and throw it into the ocean
It becomes the ocean
As long as the ocean exists, the drop of water exists
Therefore, as long as you find any part of the teachings under any religious label
Regardless of the name of the religion
The teachings still exists and survives
Then the disciple asked Buddha another question;
After you pass away, how will generations remember you? Should we make an idol of you? What material should we use? Should we use gold, silver or bronze?
To this the Buddha answered;
There is no need for an idol to be made
If you wish to, it can also be made of m&d even
As long as my teachings are practised with heart
Then the Buddha exists in everyone and everywhere
Therefore, transcends religion. In this, the message is; dont have to be particular about the name of the religion or which is more superior, avoid vanity.
I believe Tibetan Buddhism is the purest form of Buddhism.