Transfer apps, data, and settings from Marshmallow to Lollipop
If you have a pc and patience you can transfer all things from your old Android smartphone to new one.
For contacts 
Transfer your contacts from phone to your gmail ID(add a account then press sync contact in account section..Google it if u don't know)
For photos
Normally photos are stored in 


  Internal/DCIM
  Copy it into your pc 


For apps 
Download a app called App Backup Restore - transfer
And backup all your apps and transfer it to your pc 
For game/app data 
Its usually stored at internal /Android
Here you will find 2 folders one is data and other one is obb
Data contain all the data's of apps and small games
Obb contain files of large games

Or

You can use Xender or ShareIt to transfer all files from old Android to your new Android phone.
Hope I help you