A full answer depends on what plastic and what the load will be. Having a depth of 30 mm does give you a lot of options.
You can drill and tap ABS just fine, and I've had success drilling and tapping acrylic as long as I kept the tool slow so as not to overheat and warp. We have also used self-tapping screws for Delrin and UHMW with good results (and some Loctite plastic bonder). For plastics which are too brittle or too soft for direct threading, a very standard method is to place a threaded insert into a through-hole in the plastic. Helicoil, Dodge, Acme, and others make these inserts. The method of adhering the insert to the plastic depends on the process. Look at the expansion inserts on pages 24 & 25 of this Dodge catalog: http://www.afi.cc/contentonly.aspx?file=images/vendors/DodgeInserts.pdf Those seem like they would work well for you, as would the self-threading ones on page 28.
EDIT (load identified): The 6 kg cm value is approximately 0.59 N m. PEM's data for their M5 press-in threaded insert (pages 15 and 18 of http://www.pemnet.com/fastening_products/pdf/sidata.pdf) lists a torque limit of 4.02 N m for insertion into a polycarbonate plastic. That is plenty of margin. Given the large margin you could likely eliminate the Loctite step altogether.
EDIT 2 (plastic identified): With POM you can use brass threaded inserts. It is also a good candidate for direct drilling and tapping since it has low creep. If you have cyclic loading I would go with the threaded brass inserts to ensure the threads remain consistent over the device's life. If you are simply fastening items, and just need them to hold for your 6 kg cm torque load without other significant stresses, you should be fine with using thread-forming screws or the drill and tap method.