If it was a diesel I would have said DMF. But by the info you have given, it points to a worn engine or gearbox mount.
This is where you are going to need a helper.
Chock the back wheels for safety and handbrake on firmly.
Open the bonnet.
Stand to the side of the car for safety while a helper pops the clutch pedal up in a quick way while you watch for the engine block moving excessively... It should have no more than 1.5" deflection.
If there is a lot of movement then its time to get a pry bar out and check the top bushes on the upper engine mount, lever it... It should move a very slight ammount but not a lot... This is the most likely one to go.
Now get the car jacked up and on axle stands and check the gearbox mount the same way with the pry bar and a torch.
If they have very little movement then I would personally check the driveshaft cups that go into the differential housing... Too many aggresive fifth to third gear changes can damage the alloy cups so they end up with slight play.
In neutral and the front wheels off the ground with the car securely supported, get under and put your hand on the inner drive shaft. Get a helper to quckly jolt the respective road wheel forward then backwards to see if there is a lot of felt knock in the cup.
repeat on the other side for comparison. Now repeat the process with the car in fifth gear so there is some looseness before the gearbox prevents forward resistance.
It will be fairly obvious if the cups are worn.
Bleed the clutch but use an easy bleed system, other wise you end up with it drawing in air to the master cylinder on up stoke of the pedal, it's a pain in comparison to bleeding the brakes.
If you still cant find the issue, then worst case scenario it could be the clutch plate springs worn or broken or a stiff/broken spiggot finger.