Effect on msdb transaction log of running sp_delete_backuphistory for first time?

Have a server with regular db backups but strangely sp_delete_backuphistory has never been scheduled so msdb is bigger than expected. Backup history goes back 5 years in that table but only needs last 30 days of backup history. If we run sp_delete_backuphistory keeping only 30 days of history, is there any risk for the transaction log running out of space? MSDB is using simple recovery model. MSDB log file is currently 388544kb on C drive. C drive has 45gb free.