For standing on the safer side make sure you do the backup of your current rom and all your data before installing this rom.As we are not responsible for any damaged to your device.Follow below step by steps on installing Android lollipop on Galaxy Core 2.
1.You must have a custom recovery in your device CWM is fine!
2.Make Backup of your current rom from recovery.
3.Rooted galaxy Core 2.
#How to install lollipop on Galaxy Core 2 SM GT55H/M
1.After completing the above steps Download android lollipop 5.1.1 Rom from last of the post and Gapps for android 5.1.1.
2.Then place it on your SD card on your device.
3.Now turn off Galaxy Core 2 and turn ON by pressing Power button +Volume Down button to boot into recovery mode.
4.Now Press volume down button to highlight Recovery option on Bootloader then press the Power button to Select it.
5.Now your device will boot into CWM recovery.
(Note:Before you flash Cm12.1 in your device make backup of current rom in case anything wrong happens so that you can recover it).
6.Now select install zip from sd card and then select android lollipop rom and then install it, similarly flash 5.1 GAPPS in it.
7.Now go back to recovery Home then do Clear cache, Clear Dalvik cache.
8. Now reboot your device.First boot will take some time after few min android lollipop will be installed in your device.
9.Done!You have successfully flash android lollipop rom in your Samsung galaxy Core 2.