Various answers include 1/8th of the wavelength all the way down to 1/10th, but would 1/15th or even 1/20th of the wavelength be sufficient for a 60 meter (5 MHz) horizontal NVIS antenna?
Minimum height to accomplish what? It'll work right down to the ground, it'll just get lossier and lossier the lower you hang it. The exact numbers depend on your ground, and the threshold of "good enough" depends on you, your power, and who you're trying to talk to, so there's no real hard limit. Some unsourced internet numbers suggest that at 0.05 wavelength above ground you'll have about 6dB of additional loss compared to 0.2 wavelength above ground, which seems manageable.