Believe slim king (5)
I believe the answer is:
think
'believe' is the definition.
(I know that believe is a more specific form of evaluate)
'slim king' is the wordplay.
'slim' becomes 'thin' (similar in meaning).
'king' becomes 'K' (abbreviation for king in chess).
'thin'+'k'='THINK'
(Other definitions for think that I've seen before include "Believe" , "Judge, consider" , "Imagine" , "Meditate" , "Use one's mind" .)