Total voltage doesn't add up to 5V
tl; dr: There will be some IR drop in the UNO (ATMega328) I/O driver. Your measurements didn't account for that.
Why the IR Drop At The Pad?
The ATMega328 pads have a P/N pair of MOSFETs. These have an 'on' resistance Rds(on) that will insert its own IR drop when presented with a load. This would add to the total IR drop.
How much is the Rds(on)? They don't say directly. We can nevertheless figure this out from the datasheet specs for high and low drive:

High: V(oh) @ 20mA = 4.2V, IR drop is 0.8, worst-case p-FET Rds(on) is 40 ohms.
Low: V(ol) @ 20mA = 0.9V, IR drop is 0.9, worst-case n-FET Rds(on) is 45 ohms.

(Datasheet link here)
These values would be for a worst-case part at high temperature. A typical part at room temp will have Rds(on) at half of worst case, about 20-25 ohms.
Accounting For the IR Drop
We know from the 220 ohm resistor IR drop that the pad is sourcing or sinking 13.7mA. We also know the 0.320V measurement discrepancy you're seeing is due to the pad's IR drop due to Rds(on), which we can compute as follows:

Rds(on) = 0.320V/13.7mA = 23.4 ohms

Very reasonable for this part, right in the middle of typical range.
Adding all the IR drops together:

1.74V (LED forward voltage)
3.02V (220 ohm resistor)
0.32V (Pad IR drop due to Rds(on), 23.4 ohms)
sum is 5.08V total