I've seen references to a Testnet 5 or Testnet5. The last Testnet version I know about was Testnet 3, started in late 2012 by Bitcoin Core 0.7.0.
This raises two questions:
I'd assumed it was testnet5 because segnet (the segwit development testnet) was regarded as the 4th testnet. It's not strictly true though, as Bitcoin Unlimited has the nol testnet (NO Limit) and very probably there are or were other experimental testnets that I don't know about.
There's a bit of a history of skipping numbers like this: there was no testnet that was ever called testnet2 - the first two testnets were just called 'testnet' - but testnet3 was nonetheless so named - skipping the name testnet2 - because it was the 3rd testnet. (And testnet3 is still the main testnet for Bitcoin.)
EDIT TO ADD: Incidentally, the reason why we're on the third (mainstream) Bitcoin testnet is that people started to actually trade testnet coins as an altcoin, so the developers made good on their threat to reset the testnet (with a new genesis block) to help enforce the priciple that testnet coins should have no value.
The network most regarded as testnet is testnet3. However the various hard forking clients have also made their own testnets, but these are not considered "the testnet".
Testnet5 is the testnet for btc1 (aka the segwit2x client). It's parameters are defined here: https://github.com/btc1/bitcoin/blob/segwit2x/src/chainparams.cpp#L181
As for testnet4, I think that was skipped because, IIRC, Bitcoin Unlimited and Bitcoin Classic have both had their own testnets and one of them may have taken the testnet4 name.
