A word of caution, while you can get the current within the rating of the chip watch out for the power dissipation running 5 350mA LEDs is going to be very close if not over the limit.
There is a scary looking formular in the data sheet, that needs your circuit values plugging in.
As for our Mr Heny, I don't cair what you call high power, 350mA for an LED is high power. It might not be ultra high power but it is high.