The way to purge transactions that have cleared the bank and have been reconciled in BankRec is to do a period end. You can set a date for which all reconciled transactions prior to that date get purged - default this is determined by the number of days for which you keep history, set in the Company Profile.

Transactions that are still outstanding (not yet reconciled) will not be purged. Are these 5 checks still marked as outstanding?

Purging reconciled transactions does not affect the balance for today. If you are not sure about this, then definitely make a backup of your BankRec data prior to purging anything.