To obtain logs from the last 5 months that show jobs that have failed

No job history disappears when your server restarts, maybe you was told about SQL Server error log that initialize at every restart, but even previous error log does not disappear. In every case you can check your failed job this way:

select j.name,
       j.description,
       h.*
from msdb.dbo.sysjobs j join msdb.dbo.sysjobhistory h 
        on j.job_id = h.job_id 
where h.run_status = 0 -- failed
order by h.run_date;

You can check out how many history rows are preserved choosing SQL Server Agent Properties History tab.