Will high price HDMI cable makes a difference?

Depends on your other equipment.
For any normal setup, the cheap one will do.
Usually the middle price range is best. The cheapest may be very poorly made. The expensive one are selling something extra for expensive systems.

Monoprice.com. The $5.00 ones work perfectly on my 1080P set.

Honestly, if you own a 1080P set, why are you so proud of buying cheap cables?
What have you compared the $5 ones too?

AVS Forum has debated and studied the issue to death. What rch is referring to, I believe, is the general consensus about HDMI cables. According to the legitimate videophiles (of which I am not one), HDMI cables are sending 0's and 1's. Therefore, you shouldn't see a distinction between the monoprice model and the super-pricey stuff.

People who have compared a wide range of HDMI cables have reached the same conclusion. As a result, the conventional wisdom seems to be...pay $5-10 for your HDMI cables, so long as they're 1.3 compliant and can pass a 1080P signal.

Rch, apologies if I'm misinterpreting/misstating your position.