7.04 to 7.04 need help

Jose_SS

Hello, I'm new to the forum and seeking some guidance, advise, and assistance. I recently bought a 32gb ip5 to replace my 16gb ip5. The 16gb is jailbroken running on 6.0.2 firmware, unfortunately I ran out of space. This 32gb is running 7.0.4 which can be jailbroken, the only problem is I feel this phone may have been updated OTA from ios6 to ios7 so it would complicate the jailbreak. I'd like to know if I could download a 7.0.4 update, wipe the phone and update it through iTunes with the 7.0.4 firmware, allowing me to jailbreak said phone. Thanks