Climber's equipped with this and irrational not to ascend (5)
I believe the answer is:
piton
'climber's equipped with this' is the definition.
(peg used as climbing equipment)
'irrational not to ascend' is the wordplay.
'irrational' becomes 'pi' (an irrational number).
'to ascend' shows that the letters should be reversed in order (I've seen 'ascending' mean this).
'not' written backwards gives 'ton'.
'pi'+'ton'='PITON'
'and' acts as a link.
(Other definitions for piton that I've seen before include "Mountaineer's metal spike" , "Metal spike used in rock climbing" , "Metal peg used in rock climbing" , "Peg driven into rock to aid climbing" , "Peg used in mountaineering" .)