If you don’t mind running it at 20mA, then the usual calculations apply: R = (Vsupply – Vf) / If: R = (5V – 1.5V) / 0.02 = 175 Ohm. Nearest R12 series: 180 Ohm.
The reason I mention the 20mA is because the Arduino pins don’t really want to deliver the full 50mA that these are rated for (see also the Illumitune tutorial link). This may or may not be an issue for your purposes – at 20mA it’ll be a fair bit weaker (the datasheet doesn’t specify how much weaker, though).
If you did want to drive it at 50mA, you’ll want to use a transistor or the like to toggle power to the LED. Fortunately, SparkFun sell a kit that has everything you’d need – Max Power IR LED Kit except it uses the 950nm IR LED, so you’d have to swap that out with this one if you need the 850nm, or build your own circuit based on the Max Power schematic (it is a pretty simple one, but if you don’t already have the components laying around, that kit is neat and tidy, and a timesaver).
