VCC sets the current

One segment

A lit segment is a row of four things: VCC, the 595's output, a 150 Ω resistor and a red LED, to GND. The LED takes about 2 V (ARKLED's sheet gives 1.9 to 2.5 V, 2.0 typical). What is left, VCC minus 2 V, falls across the resistor and the output, and that sets the current.

With a perfect output, the resistor alone:

• 3.3 V: (3.3 − 2.0) / 150 = 8.7 mA
• 5 V: (5.0 − 2.0) / 150 = 20 mA

A real output is not perfect. Nexperia's datasheet has its HIGH output at 4.32 V typical, 3.84 V at worst, while supplying 6 mA from 4.5 V: about 30 Ω inside the chip, typically, and up to 110 Ω. Added to the 150 Ω, a segment at 5 V takes about 17 mA, and no less than about 11.5 mA. The datasheet gives no such row at 3.3 V, so 8.7 mA stands there as the most it can be.

The LED's own limit is 20 mA continuous, so either supply is fine for a segment.

Eight segments, one chip

Every lit segment's current comes in through the 595's VCC pin, and the datasheet's absolute maximum for that pin is 70 mA, for the whole chip. That is the limit a digit meets.

At 3.3 V, even an 8 with its dot, eight segments, is 8 × 8.7 = 69 mA at the very most: inside 70.

At 5 V, 17 mA a segment means four segments fit, 67 mA, and five do not. An 8 is seven segments, about 117 mA typical and 81 mA on the weakest chip. It lights, and it is past the chip's rating. Nothing here has been measured; these are datasheet numbers and arithmetic, and they say an 8 at 5 V is outside what the chip is sold to do.

So which VCC

VCC also decides what the chip reads as HIGH: 0.7 of VCC. At 5 V that is 3.5 V, more than a 3.3 V board's pins give. So the choice is made for you:

On an Uno it works at 5 V, brightly, outside the datasheet when most segments are lit. For a display left running for days, a 3.3 V board keeps it inside every number on this page.