Cold gas-phase water has recently been detected in a cold dark cloud, Barnard 5 located in the Perseus complex, by targeting methanol peaks as signposts for ice mantle evaporation. Observed morphology and abundances of methanol and water are consistent with a transient non-thermal evaporation process only affecting the outermost ice mantle layers, possibly triggering a more complex chemistry. We present the detection of the Complex Organic Molecules (COMs) acetaldehyde and methyl formate as well as formic acid and ketene, and the tentative detection of di-methyl ether towards the methanol hotspot of Barnard 5 located between two dense cores using the single dish OSO 20m, IRAM 30m, and NRO 45m telescopes. The high energy cis- conformer of formic acid is detected, suggesting that formic acid is mostly formed at the surface of interstellar grains and then evaporated. The detection of multiple transitions for each species allows us to constrain their abundances through LTE and non-LTE methods. All the considered COMs show similar abundances between $sim 1$ and $sim 10$ % relative to methanol depending on the assumed excitation temperature. The non-detection of glycolaldehyde, an isomer of methyl formate, with a [glycolaldehyde]/[methyl formate] abundance ratio lower than 6 %, favours gas phase formation pathways triggered by methanol evaporation. According to their excitation temperatures derived in massive hot cores, formic acid, ketene, and acetaldehyde have been designated as lukewarm COMs whereas methyl formate and di-methyl ether were defined as warm species. Comparison with previous observations of other types of sources confirms that lukewarm and warm COMs show similar abundances in low-density cold gas whereas the warm COMs tend to be more abundant than the lukewarm species in warm protostellar cores.
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