Triggering a relay using a transformerless power supply

Following the calculations here: http://www.daycounter.com/Circuits/...Supplies/Transformerless-Power-Supplies.phtml

With the circuit as follows:


Using:
Vrms: 120V, 60Hz
R1: 6.8 ohms
C1: 1uF 250V Metal film
C2: 470uF 25V Electrolytic radial
D1: 1N5818
ZD1: 1N4733 5.1V 1W Zener

The calculations yielded:
Iout: 25.8ma

I have a couple Kest# KS2E-M-DC5 relays, 5V coil with 130 ohm resistance, or about 38ma max. My question is very simple: Must I attain 38ma in foward current in order to trigger the relay? or will 25.8ma suffice?

Building a couple blackout lights that uses a relay to monitor line voltage that closes a switch to an LED when power fails

Ideally, a 5v relay will pull in at 5(2/3)v and drop out at 5(1/3)v.

It's like a car clutch. The top 1/3 of pedal travel is fully engaged and the bottom 1/3 is fully disengaged.