Wow, CTH. This brings back memories, what a great little amp with some neat features like the self zeroing output diamond buffer.
Anyhow, I'm not Alex, but the CTH uses a class AB diamond buffer with approximately 20mA idle. It should peak out around 40mA before exiting class A. I am not sure what the voltage swing is, but for the HE-500 it shouldn't matter, it will be current limited.
I would guess the voltage swing should be about 13Vp-p, roughly 5Vrms. I'm guessing roughly 185mW rms. Heat in the small enclosure is a constant battle, I'm not sure it can sustain that. Note, no calculations done, and no measurements taken. I'm not really sure if it can hit that before it clips. Anyhow, for 38ohm you're likely looking at around 60mW of class A. That should land you around 105dB-ish before coming out of class A.
Depending on how much SPL headroom you actually need or want to target, should dictate your headphone amp requirements. I guess if you need 120dB peak out of your HE-500, then the popular DIY amps out there are EHHA and Beta22. The SOHA2 should land you around 112dB, in stock form. You can get more with a bigger heatsink.
Edit: keep in mind, it's all theoretical. One would need to bench the amp to see where it lands in terms of THD to determine what's acceptable or not.