1/2" copper to 1/2" pex

I am in the middle of a bath remodel. The original copper lines in the wall for the shower had the 1/2" supply for hot capped, probably due to a leak or low pressure. It was done when the house was built. They put a T on the garden tub stub up which is in the middle of the floor and ran that line under the shower pan to the shower wet wall next to the cold supply. When I tore out the tub and shower I discovered that I have no way to supply the new shower. The water heater is on the other side of the house, and this remodel bath has no attic.
I don't want to tear up the slab if possible.
Can I run 1/2" pex off a 1/2" copper supply under the sink through the wall and still get enough water to supply a 3/4" valve and 3 separate volume controls feeding 3 shower heads? Will I lose volume through the pex connection, or the 15' of pex I need to do the run?

Thanks

You may need to rethink your shower plans. a 1/2" supply is probably marginal, and if you actually run it through 1/2" pex, almost certainly - it would depend on how many gpm the heads require. The ID of pex is smaller than copper (the OD is the same, but the pex wall thickness is considerably bigger). If you ran 3/4" pex, you'd have about the same volume as the 1/2" copper, and even if you extended it in copper, 1/2" might not be big enough. 1/2" pex is probably good for a max of 4-5 gpm. Now, mixing it with some cold would allow that to go up some, since you'd have two independent lines feeding the valve, but it depends on how hot you run your water heater and how much it cools, and how cold the cold is the mix you'd end up with.

Jim,
My fears also. Although I spoke to manufacturer, Danze, and they say output should be around 12gpm with 1/2 supply to a 3/4" valve. At full on I will have (3x 1.5)body sprays + 2.5 +2.5 =9.5gpm. I don't think it will be run with all 5 heads at the same time. I also have 3 volume valves (one for each piece.) The problem I have is not being able to find gpm for pex at 45 lbs.