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I have changed my cassette and chain, as well as having had two different LBSes do the indexing, but the chain would still skip when on the fifth sprocket (working up from the smallest).
I have since changed the large chainring to a new one, and thought that that would solve the problem. But no. On yesterday's ride (the first in a few weeks), much to my frustration, the skipping was just as bad. And always on the same sprocket.
What's up with that? How the &*!$ can I get the transmission working smoothly?!? 👿
Possibly a bent mech hanger. Have you had it checked?
Always worth fitting new cables too.
The mech hanger is brand new, and I think (I'll check) that the cables are as well...
Check the mech hanger anyway. I've had to straighten new ones....
jockey wheels?
+1 mech hanger or maybe a bent tooth on the sprocket?
I've recently been trying to eliminate similar but it wasn't dropping down to the smaller cogs from the middle, i've just fitted some new Jagwire cables and it shifts like clockwork now, Yours could be any of the above though, Jockey wheels, bent tooth on the sprocket????.
Bought a hanger straightner from wiggle, should have bought one years ago.
friction in the cable outer on the last before the RD? Does it index really cleanly to and from this sprocket? I replace mine at the slightest hint of poor shifting and skipping. Otherwise hanger alignment.
Loose free hub / wheel bearing......
Buy one of these:
[IMG] 
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You won't regret it.
Could be a frayed cable snagging in the shifter but my first thought was mech hanger.
Might be a stiff link in the chain when it was joined
Wouldnt a bent hanger affect more than one gear? OP says its always the same gear and bent hangers in the past for me have affected more than one gear. Have a look at that sprocket for any teeth with a burr on it, i had a new one which had a couple burrs on the teeth and that took me bloody ages to find. Good luck OP
I've seen a stiff link and dirty cables cause skipping on otherwise new transmissions
Single sprocket fitted the wrong way around?
limit screws.
that can have a massive effect on shifting performance because if you have the limit too tight on the higher gears as it moves through the block the tolerances go out of whack and eventually you get the skipping.
parktools.com has a step by step guide on how to set it up. just follow that. its 5 minute job. you would be surprised at how many bike shops cannot do this properly.
How do the limit screws affect anything other than top and bottom gears?
OP - is it slipping or skipping? i.e. do the pedals jump forwards under load because it's skipping over teeth, or is the chain trying to drop or climb into the next gear?
Will it do it on the workstand, or just when riding?
limit screws.
that can have a massive effect on shifting performance
no they cant.
limit screws.
that can have a massive effect on shifting performance because if you have the limit too tight on the higher gears
The limit's just a hard stop though isn't it? Too much cable tension against the limit would do this but then you'd not get into the second gear.
(have been having a similar problem with my own road bike)
Stiff/bent link
b screw adjustment
indexing