Does anyone know how to set 6 different PWM values to channel 5 on the Avionic RCB6i instead of just 3? I want to use more modes with my APM but I'm limited to just channel 5, which by default only provides 3 modes.

If you are good at soldering then you can remove that  3 mode switch and replace it with a potentiometer or slider switch like one found on quantum i8 . Before doing any mod on shell of transmitter make sure you new mod works properly .

Don't really want to do any modding. Is there no in built way to do this?

To get 6 flight modes, you would want to mix a 2-position switch and a 3-position switch. Unfortunately, the 6i offers very limited programming capabilities (which is why I switched to a 9XR). It has a few pre-programmed mixes like Delta, V-tail and Flaperons but I don't think you can set up custom mixes on it. One option would be to add a pot, as was mentioned here, but that makes mode changes tricky as there is no tactile feedback when you change modes, and you have to judge the potentiometer position by looking at it. A 6-position rotary switch (like the one on the Quanum i8) would be better but I don't know if it can be installed the 6i.

Bro its a very easy job.
5 min max.
You need a 6 pos switch
and nothing else.