Download GPU-Z and see if OpenCL is unchecked. In GPU-Z, most if not all, AMD GPU Cards have both OpenCL and DirectX Checked marked.
If unchecked than uninstall the GPU driver using DDU in Safe Mode with the internet disconnected until you installed the complete AMD driver package again.
Seems like the ATI Mobility Radeon and ATI Radeon AMD Drivers for the HD5450 are identical from here: ATI Radeon™ HD 5450 Drivers & Support | AMD
Try installing the BETA one from 2016 and see if OpenCL is checked marked.
If that doesn't work, make sure you have the latest BIOS and Chip Set versions installed for your motherboard.
I uninstalled my Desktop PC GPU driver using DDU ( https://www.amd.com/en/support/kb/faq/gpu-601 ) in Safe Mode with the internet disconnected, And then I reinstalled my GPU driver (15.7.1 WHQL)
GPU-Z shows that OpenCL is Active, But OpenCL IS Grayed Out On PhotoShop CC 2018.
In addition, My graphics card is supported by photoshop ( https://helpx.adobe.com/photoshop/kb/photoshop-cc-gpu-card-faq.html ) And many users on the Internet have said that Radeon Software Crimson Edition Beta (3/1/2016) does not support opencl, So I didn't test Crimson Edition Beta Driver!
If GPU-Z is showing OpenCL active than the problem is with Photoshop CC 2018.
Also, I believe, all AMD Drivers support OpenCL.
You may, for troubleshooting purposes, install the BETA and see if Photoshop recognizes OpenCL. The BETA was the new AMD Driver format Crimson that came out after Catalyst.
If the same results then you can reinstall the 15.7 version which is WHQL Driver.
EDIT: Reread your original post. Notice that you did try to activate OpenCL correctly in Photoshop.
IF both AMD Drivers shows your GPU card as having OpenCL active in GPU-Z but not in Photoshop.
In my personal opinion, it could be the AMD Drivers are too outdated and not compatible with Photoshop anymore as far as OpenCL is concerned.
By the way, Make sure your Windows version is fully updated to the latest via Windows Update.
See if you can borrow, for testing purposes, a newer AMD GPU card and see if in Photoshop OpenCL can be activated. Something like a RX series card. That may indicate that the AMD Driver from the HD is too outdated and not compatible since you will be using the latest AMD Driver.
I have installed the beta version of Driver (Crimson Edition 16.2.1 Beta - 3/1/2016):
Unfortunately the beta version does not support Open CL.
And finally, after spending a lot of time I was able to remove the beta (I got a Sync Out of Range error when loading into Windows), And back to the previous version.
I do not recommend installing the beta version to anyone!
The same issue:
One possibility is that Photoshop probably needs OpenCL version 2.0, but the OpenCL version reported by GPU-Z is 1.2. I think you need a newer GPU and the Adrenalin driver to fix this.
What are the minimum graphics processor and display requirements?