Why can't my rear shifter shift into low gears?
It's a little unclear whether the shifter is refusing to get into the lower gears based on what the indicator is showing or if it's indicating lower gears than 5 but nothing is happening in back. Also I'm assuming by "lower" you mean larger cogs and that you don't have a Rapid Rise rear derailleur.

If the shifter is clicking from gear to gear but not moving the rear derailleur into the large cogs, it's likely you need a bunch more cable tension. This is one of the more common break-in type adjustments bikes need. There are plenty of questions here about this, but the basic process is loosen the RD cable, screw the barrel adjuster(s) on the shifter and/or RD in, and fasten the cable back so that you have all the slack taken out, barely taut, then use the barrel adjusters to fine tune from there.

If you mean that it's having a hard time getting into the small cog (the high gears), then check to make sure there's not a cable housing end hung up on either a housing stop on the frame or the where it enters the shifter or RD.

If you did happen to have Rapid Rise, either of the above problems can still occur, but the symptom that goes with each solution would be switched in terms of which end of the cassette you can't shift into.

Friction in the housings could cause this problem too but it sounds like you've eliminated that. Make sure you've checked all the RD housings - bikes can have 1, 2 or 3 of them depending on the design.