What happens when I play Icathian Rain choosing a Recruit at Heisho, Shell of the World once and Irelia, Fervent in base five times? How many times do I pay for deflect?

You will not pay for deflect.

While your spell or ability chooses a unit at Heisho, Shell of the World, you ignore deflect while paying for the spell. Ignore, in this context, means you treat deflect on the specified units as being inactive, like it’s turned off temporarily. In the case of Heisho, it doesn’t specify any units whose deflect to ignore, so you ignore all instances of deflect on units.

This only applies to the specified spell or ability. You can’t play a spell or ability choosing a unit at Heisho, and then play another one choosing a unit at another location and not at Heisho and still ignore deflect. Only while at least one target of the spell or ability is a unit located at Heisho do you ignore deflect while paying costs for that spell or ability.