Not sloshed, but serious (5)
I believe the answer is:
sober
'serious' is the definition.
(sober can mean sensible or serious)
I don't understand the remainder of the clue.
Can you help me to learn more?
(Other definitions for sober that I've seen before include "Staid; clear-headed" , "Sensible - clear-headed" , "Sedate and rational" , "Sedate - staid" , "Temperate" .)