I have acquired a PS Vita which hasn’t been out of the box since it was manufactured. Never used and never charged. Given that the lithium cell has been in there for the best part 5 years, am I safe enough to charge it?

I'd imagine the charging circuitry should be able to allow a safe test with the provided charger. Monitor it for unusual warmth or swelling of the battery, those seem to be the first signs of an possible failure, and don't leave it unattended overnight.

For some Apple laptops with tight tolerances, things like the trackpad no longer accepting clicks was a sign a failing battery was swelling below that area.

Don’t leave it in, on or near things that could be damaged by sudden heat or a small(ish) fire. A metal tray on a non-burnable surface would be a safe place to experiment with charging an old lithium battery.

If the battery still has some charge, enough to briefly power on the unit, then there is a better chance of the battery being usable. If the battery is so dead that the unit cannot even begin to power up, then the battery may be discharged deeply enough to be internally degraded.

In any case, charge with caution. And even after being charged, keep an eye on it through the next few use and recharge cycles. Do not be leaving it on the sofa cushions or bedside while you go out for dinner.