Induction coil has to be built so that it only resonates with circuit capacitances above ~ 5-10 MHz.
Why not use optical coupling? There are optical IR links that carry > 10 Mbps over several feet. They use LEDs and PIN photodiodes. Try to google available commercial models.
Over 5 cm you can possibly use a capacitive transfer, by trying fast opamps to pick up several mV,either directly your baseband or modulated on a suitable carrier, from 1 Hz up to 900 MHz.