tail -f /var/log/file1 -f /var/log/file2

tail -f /var/log/file1 | grep '(pattern1|pattern2)'

tail -f /var/log/file2 | grep '(pattern3|pattern4|pattern5)'

RED='33[0;31m'
BLUE='33[0;34m'

 tail -fn0 /var/log/file1 | while read line;
    do
       if echo $line | grep -q '(pattern1|pattern2)';then
          echo -e "{$RED}$line"
       fi
    done