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#!/bin/bash

sum=0
while IFS=, read -a fields; do
  if [[ ${fields[12]} = "$1" ]]; then
    (( sum += fields[5] ))
  fi
done < file.csv

printf 'sum: %d\n' "$sum"

You can shorten the if..then..fi using short-scircuit logic if you prefer ex.

[[ ${fields[12]} = "$1" ]] && (( sum += fields[5] ))

There's no need to skip the header line explicitly since it will fail the ${fields[12]} = "$1" test