Here is the related info (this is using the 7941/7961 as an example only) and using the Firmware 8.3(3)SR2 as an example only. Your process will be the same but will include newer Firmware, something like 8.5(2) or whatever matches your new build :)
For CCM 4.X;
Installing the Firmware Load
Before using the Cisco Unified IP Phone models 7941G or 7961G with Cisco Unified CallManager release 3.3 or later, you must install the latest firmware on all Cisco Unified CallManager servers in the cluster.
When using Cisco Unified CallManager Release 5.0 or later
For Cisco Unified CallManager 5.0, you must do all software installations and upgrades by using the Software Upgrades menu options. The system can upload and process only software that Cisco Systems approved. You cannot install or use third-party or Windows-based software applications that you may have been using with a previous version of Cisco Unified CallManager with Cisco Unified CallManager 5.0.
Using your web browser, login to the Cisco IPT Platform Administration web page
Under the Software Upgrades menu, select Install/Upgrade.
Fill in the appropriate values in the Software Location section for the file you downloaded above, and click Next.
In the Available Software drop-down box, select the file you downloaded above, and click Next.
After validating the MD5 has the correct value, click Next.
In the Warning box, verify you have selected the correct firmware, then click Install.
Check that you received a Success message.
When Using Cisco Unified CallManager earlier than Release 5.0
Login to the console of the Cisco Unified CallManager Server where you downloaded the installer.
Note the location where you saved the downloaded file.
Double-click the file to start the installation.
In the Welcome window, click Next.
In the License Agreement window, click Yes.
If a Read Only File Detected window pops up, click Yes.
After the installation finishes, click OK.
Reset all corresponding devices.
Cisco IP Phone Model 7941/7961 Alternate Firmware format
The Cisco IP Phone Model 7941G/7961G Firmware version 8.3(3)SR2 is also supplied in a zip file, as an alternative in case a Cisco Unified CallManager is not available to run the executable installer program. The name of this file is cmterm-7941-7961-sccp.8-3-3SR2zip.
After unzipping the firmware files, they should be manually copied to the appropriate directory on the TFTP server.
From this good ReadMe;
Hope this helps!