Why would a part be available as 4.99k and 5k?

The E96 series of preferred numbers contains the 4.99 values.

E96 values (1% tolerance) 1.00, 1.02, 1.05, 1.07, 1.10, 1.13, 1.15, 1.18, 1.21, 1.24, 1.27, 1.30, 1.33, 1.37, 1.40, 1.43, 1.47, 1.50, 1.54, 1.58, 1.62, 1.65, 1.69, 1.74, 1.78, 1.82, 1.87, 1.91, 1.96, 2.00, 2.05, 2.10, 2.15, 2.21, 2.26, 2.32, 2.37, 2.43, 2.49, 2.55, 2.61, 2.67, 2.74, 2.80, 2.87, 2.94, 3.01, 3.09, 3.16, 3.24, 3.32, 3.40, 3.48, 3.57, 3.65, 3.74, 3.83, 3.92, 4.02, 4.12, 4.22, 4.32, 4.42, 4.53, 4.64, 4.75, 4.87, 4.99, 5.11, 5.23, 5.36, 5.49, 5.62, 5.76, 5.90, 6.04, 6.19, 6.34, 6.49, 6.65, 6.81, 6.98, 7.15, 7.32, 7.50, 7.68, 7.87, 8.06, 8.25, 8.45, 8.66, 8.87, 9.09, 9.31, 9.53, 9.76.

So the question is really, who wants a 5.00 value? I've never seen 5 kΩ specifically but I have seen specialty values used for things like ADCs, voltage dividers for multimeter voltage ranges, etc.. Many PLCs use a 250 Ω resistor to convert 4 - 20 mA to 1 - 5 V for their analog inputs. This too is not a standard value.

The difference between 4.99kOhm and 5kOhm is of the order of 10 ohm, ie a 0.2% change. The resistor tolerance required, as you mentioned, is 0.1%. So if 0.1% tolerance is allowed, a change of 0.2% would disrupt the accuracy. This means that the separate valued resistors are necessary.

I agree with the posts above. All the other values listed in the Datasheet except 500Ω, 5kΩ and 50kΩ are part of the E-series of Resistors.

Because the resistor is used for "unity gain operational amplifier circuitry" or "voltage references" I assume there are cases where an integer resistor ratio is needed e.g.: 20kΩ / 5kΩ = 4.00. Which otherwise is not easily achievable without combining multiple resistor values in series/parallel.

Therefore they introduced the 0.5 value in addition to the values from the E-series.