What size cassette

You might need to stick a medium cage on to fit a 32t but I am no expert. I think its got something to do with the size/drop of your front rings too.
 

slowmotion

Quite dreadful
Location
lost somewhere
We need to know the number of teeth on:
Your biggest chain ring
Your smallest chain ring
Your biggest cog on rear derailleur
Your smallest cog " "

With that, you can see what would satisfy the official 105 gear rules and what you might get away with.
 

robgul

Guru
In most cases you can add 2 teeth to the number that Mr Shimano gives as the max sprocket size .... the key is whether there's enough on the B-screw to push the mech back so that it doesn't mesh when in largest sprocket/smallest chainring (although there are tricks to fix this - a mech extender (Wolf at a price - or ebay for a couple of quid) OR the old MTB option of screwing the B-screw in from the other side to gain the tickness of the screw-head)

Rob
 
A 32 tooth large sprocket will fit that set up without having to change the RD, or add a hanger extender, most ‘off the shelf’ cassettes with a 32 tooth big sprocket, will be 11-32. It will work as long as you don’t go to a 53 tooth chainring.
 

Joffey

Veteran
Location
Yorkshire
I think it has a 50/34 chainring
You'll be fine then - just check your chain length and if it's tight avoid the 50 when in the 32.
 

Dogtrousers

Kilometre nibbler
There are lots of models of 105. I picked this at almost random (I chose a 10sp rather than the latest R7000 11sp, which I know goes up to 34 max sprocket)

105 5701 10-Speed Rear Derailleur (Link https://www.wiggle.co.uk/shimano-105-5701-10-speed-rear-derailleur-1/ )
Maximum Low Sprocket: Short Cage: 30T; Medium Cage: 32T
Maximum Front Difference: Short Cage: 16T, total capacity 34T; Medium Cage: 22T, total capacity 40T

The required capacity for a 11-32, 34/50 is 50+32-11-34 = 37

So yes, provided that's a medium cage in the picture, which it is (have a look at some photos on line to double check), then you can fit an 11-32 cassette with a couple of teeth capacity to spare.
 

robgul

Guru
mm - I wouldn't set any bike up where I had to stay out of certain combinations. Asking for serious trouble - at least with me,
Hmm - cross-chaining isn't good for chainrings, sprockets or chains - pretty much the opposing 2 or 3 sprockets ought to be out of bounds to minimise wear and damage on anything 9 speed and greater. That's my view, others may diasagree!

Rob
 

Dogtrousers

Kilometre nibbler
Hmm - cross-chaining isn't good for chainrings, sprockets or chains - pretty much the opposing 2 or 3 sprockets ought to be out of bounds to minimise wear and damage on anything 9 speed and greater. That's my view, others may diasagree!

Rob
Some pro MTB'ers run short chains that could potentially wreck components if the wrong gear is selected in error. Like Batman and Robin they are special people and you shouldn't try this at home. A moment's inattention could leave you stranded. I'd never run components that could wreck my bike if I made a mistake.
 
Location
London
Hmm - cross-chaining isn't good for chainrings, sprockets or chains - pretty much the opposing 2 or 3 sprockets ought to be out of bounds to minimise wear and damage on anything 9 speed and greater. That's my view, others may diasagree!

Rob
am assuming like dogtrousers that you were speaking of combinations which might "jam", not just cause a bit of rattling/efficiency loss. If you are rob, though this might be fine for you, I don't trust myself.
 
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