True. The figures that I used were for the combined primary and secondary windings. I used the regulation quoted in the data sheet to workout the equivalent secondary resistance, and used that alone. The total copper loss is quoted as 18 W for primaries and secondaries.But note that the secondary copper loss for the rated RMS current is 8.36W total (both windings) so if you go above that value you may cause overheating and deterioration of the winding insulation.
At full load of 5.333 A, the secondary copper loss is 5.333^2 * 0.1469 = 4.178 W per winding.
The primary current is 5.333 * 15 * 2 /230 = 0.696 A, so the primary copper loss is 0.696^2 * 5 * 2 = 4.84 W
It doesn't quite add up, because those figures add up to around 13 W, while the data sheet quotes 18 W total copper loss.
I've gone back and looked at RMS secondary current. The RMS current does depend a bit on the series resistance. If there is very little series resistance the capacitor charges very fast, increasing the RMS current. With an equivalent resistance of 0.152 Ω, there is 13.3 W of heating at 5 A DC, which represents 74% of the maximum heating. The RMS secondary current is 9.35 A, which gives 77% of maximum heating.
I think that either RMS current or transformer heating is a valid approach, but estimating the current waveform is not all that easy, and it makes a big difference to the peak current.