Drivers for Radeon 5000 series.... ...

Support Graphics & Display
1

Use to make a suitable replacement for nvidia NV40 (GeForce 6, GeForce 7) used in HTPC running mythtv?

i.e. XFX AMD Radeon HD 5450 1GB GDDR3 VGA/DVI/HDMI Low-Profile PCI-Express Graphics Card [HD545XZQH2;HD-545X-ZQH2]
or possibly
AMD Radeon HD 8490 Low Profile Graphics Card - 1 GB DDR3 - 64-bit

2

Actually for the best experience you want the amdgpu driver support. Which means cards with GCN 3rd generation architecture (or later), those were introduced with the 300 series (but also some 200 series card feature GCN 3rd gen). A good overview is on Wikipedia:

and

(Note how the series are mixed with GCN 1st, 2nd and 3rd gen cards!)

amdgpu was later also backported to some (?) GCN 2nd gen cards, but I wouldn’t recommend going that route.

3

Ordered Radeon HD 7450 2GB VGA HDMI DVI PCIe Video Card+Low profile Bracket

Thanks for the advice…!