The datasheet you submitted is for a common anode part.
If this was a typical 7-segment display, the way it is usually used is that the commone anode, pins 1&5, are connected to 3.3V or to 5v.
Then a current limiting resister of say 330 ohm is connected from each of the segment leads to an output pin on the arduino (or, to a shift register output pin). When the pin is low, the segmet will turn on. When the output is high, it will turn off (as both sides of the LED are now high).
However, your part has 3 LEDs per segment, so it will need a higher voltage, the spec sheet shows 6-7.5.
For that you will need a part that can withstand a higher off voltage and not be damaged, such as
a tpic6b595 open drain shift register, which can take 50V. Or, put an NPN transistor at the bottom of each cathode, which is basically what the output of the tpic6b595 has.
There are some other open collector/open drain parts as well.