Close to indistinguishable, however, with singular distinctive character (5)
I believe the answer is:
ethos
'distinctive character' is the definition.
(I've seen this before)
'close to indistinguishable however with singular' is the wordplay.
'close to' indicates one should take the final letters (the 'close' to the word).
'however' becomes 'tho' (I've seen this in another clue).
'with' means one lot of letters go next to another.
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
The final letter of 'indistinguishable' is 'e'.
'e'+'tho'+'s'='ETHOS'
(Other definitions for ethos that I've seen before include "Cultural spirit" , "Spirit (of an age/culture)" , "Distinctive group spirit" , "Spirit (of, eg, an age)" , "Characteristic spirit of a community - for those" .)