...some content...
                   The mail system

<slavicatomic118@hotmail.com>: host mx1.hotmail.com[65.54.188.94] said: 550
    Requested action not taken: mailbox unavailable (in reply to RCPT TO
    command)

...some content...
                   The mail system

<oki88@optimumpro.net>: host viking.optimumpro.net[79.101.51.82] said: 550
    Unknown user (in reply to RCPT TO command)

...some content...
                   The mail system

<sigirna_luka@yahoo.com>: host mta5.am0.yahoodns.net[74.6.140.64] said: 554
    delivery error: dd This user doesn't have a yahoo.com account
    (sigirna_luka@yahoo.com) [0] - mta1172.mail.sk1.yahoo.com (in reply to end
    of DATA command)

...etc.

grep -A 2 "The mail system" mbox_file

grep -A 2 -B -2 "The mail system" mbox_file

grep: -2: invalid context length argument

grep -A 4 "The mail system" temp.txt | grep -v "The mail system" | grep -v '^d*$'

sed -n '/The mail system/{n;n;p}'

sed -n '/The mail system/{n; n;p; n;p; n;p}'

sed -n '/The mail system/{n;n;N;N;p}'

sed -n '/The mail system/{n;n;N;N;p;i--
       }' > output-file  # or | ...

<slavicatomic118@hotmail.com>: host mx1.hotmail.com[65.54.188.94] said: 550
    Requested action not taken: mailbox unavailable (in reply to RCPT TO
    command)
--

grep -A 2 -B -2 "The mail system" mbox_file

grep -A 2 -B 2 "The mail system" mbox_file   # This will work please check

grep -A 2 "The mail system" mbox_file | tail -n +3

perl -ne 'print if( (/The mail system/ && ($end=1))..!$end-- )'