Skipping chain on 5sp setup

Hi all.
I just built up a bike out of parts I've had laying around and I'm coming across an issue that has me stumped. Basically the chain is jumping off the freewheel on the two smallest sprockets under load, but not the larger three. I'm running a wilko 5-7 speed chain on a (what looks in really good condition) 5 speed Regina block.
Google has me thinking that either:
The chain I'm using has the wrong pitch, do I need a 1/8? The freewheel block has no splining and looks large and chunky.

Or,

The freewheel is worn and so a new chain isn't binding, does this sound correct? If so I recon on grabbing a new freewheel as well as a new chain should get me going...

What is most likely?

Cheers.

Get a new chain and freewheel.

do I need a 1/8?

No. 1/8" is solely for singlespeed (or hubs gears). Pitch is the distance between the pins, not the width of the chain.

What does your chain wear tool say?

Is the chainring worn? They tend to wear faster than freewheels and cassettes: two rings vs five (in your case) rear sprockets, so the rings get more use.

this

Chain is good according to wear and crankset is brand new. And good to know info too.
Like others are saying it looks like I might have to actually spend a couple of quid on a new freewheel then.

Thanks!