Indexing gears for a newbie

[Tim Hall]

So after much adjusting I've reached this point -
Bike is in 4th gear whether the twist grip says 5th or 4th
Shift to third - fine
Shift to second - fine
Shift to 1st - jumpy but does it.
Back to second - fine
Back to third - Nada
Back to fourth -takes it to third
Back to fifth - takes it to fourth.....

I am carrying on with the fine tuning but if the above suggests something obviously wrong to any of you that'd be helpful. In spite of not being able to get this quite right I am rather enjoying myself....

When shifting up (going to smaller sprockets), nearly all rear mechs use the spring tension to do the work. When shifting down (going to larger sprockets) the work is done by the rider's muscles pulling the cable (a few, Rapid Rise from Shimano, work the other way). Your symptoms suggest that there's some resistance in the gear cable which the spring is struggling to overcome. New housing seems a good bet.