Will a specific denormalization increase performance in a specific scenario?
The question is: will it boost the performance of select to split the
  table into five tables each corresponding to one of the five possible
  values of z?


Yes, you could use partitioning here. Partition elimination will kick in. The partitioning will act as a leading index column.

Which brings me to the following point: Just add z as the leading column to all indexes. As you always filter on z (using an equality predicate) this will only help. (Except, if the index was unique anyway like an index on an ID column).

I'm generalizing a bit here like always with databases, but make sure to add filtering on z to your indexes.

Other techniques apply as well, of course, like making indexes covering.

I don't see the necessity for creating 5 tables, or using partitioning here. I can see how that might improve performance by a few percent, though, because z no longer needs to be stored.

If your app is generating enough load that a few percent of load matter, then your server is overloaded anyway by my definition. Still, it is worth a try if you don't care about increased development and maintenance costs.