so you are telling us that doing a
insert into archive_table
from main_table where filtering_column = date_to_archive
takes 5 minutes?
or that it takes that amount of time retrieving the records onto your SSMS window?
if the second then try the first one - onto a temp table and see how long it takes. and if it still takes more than 1 second give us the actual explain plan of the execution alongside table DDL (table and indexes)
Regarding archive process you need to tell us where you wish to archive to - same db, same instance, different server or filesystem
and also if people would actively and daily query that archive table or if it can really be archived (e.g. column compressed) with minimal impact