I'm sorry about that. Your only hope is iCloud backup. If there is iCloud backup made from previous iPhone, then you can restore your phone to that backup. You can erase this new iPhone and see if there is any backup available. Note : This process will delete everything from current iPhone.
Go to Settings > General > Reset and tap Erase All Contents and Settings. After erasing the iPhone, it will ask you to setup it. While setting up, select Restore from iCloud and if there is any backup available, it will restore to it.
After selecting Restore from iCloud, you have to sign in to the same iCloud account you used on the old iPhone 5 and this will only work if there is any backup available.
If that didn't work, then go to www.icloud.com and login to your iCloud account. Click Photos and see if you see them there ?
If you're unable to get them or if you don't see them on iCloud.com, then I'm sorry they are gone. If you have any questions, please let me know and I will answer them.
If you are not satisfied with the answer I provided, please don't rate me bad or poor as it will badly affect my job here.