I had the same hardware and the same problem.
The Microsoft Wireless Keyboard I have already sold since its frequently used keycaps got their letters erased. Amazingly someone still wanted to buy it. So parted from it giving respect to its value, but not to its quality.
I still have Microsoft Wireless Laser Mouse 5000 Model 1058 and there isno LEDs or red light in the bottom like in the optical mouses to indicate it is working or has good batteries. The laser in this device is just invisible. Not seen with cellular camera either, which you can use to test if RF remote controller transmits. Receiver however should have its green LED turned on to indicate connection between mouse and receiver.
I just verified the problem is that Microsoft Wireless Laser Mouse 5000 is not compatible with Mouse and Keyboard Center that started to replace IntelliPoint and IntelliType Pro software during Win7. For Win 7 you can have either one or
maybe even both installed, but when Win8 came IntelliPoint and IntelliType were totally replaced by Mouse and Keyboard Center.
I also tested that even with Win10 64-bit IntelliPoint 8.2 installs and launches but fails to get mouse and receiver connected, eventually turning off blinking LED of receiver.
To prove incompatibility between Microsoft Wireless Laser Mouse 5000 and Mouse and Keyboard Center read:
https://www.microsoft.com/accessories/en-us/support/troubleshooting/mouse/supported-devices
In the list the only Microsoft Laser mouse that works with Mouse and Keyboard Center is Microsoft Natural Wireless Laser Mouse 7000.
There is also a list here is the compatibility and incompatibility, but it lacks some entries. Like Microsoft Wireless Laser Mouse 5000. So consider the first source more reliable.
https://en.wikipedia.org/wiki/Microsoft\_Mouse\_and\_Keyboard\_Center
IntelliPoint 8.2 Mouse Software supports Microsoft Wireless Laser Mouse 5000 inWin7, Vista or XP.
https://www.microsoft.com/en-us/download/details.aspx?id=26948 (note there is different link for 32-bit)
https://en.wikipedia.org/wiki/IntelliPoint#Supported\_mice
IntelliPoint 7.0 Mouse Software is the last one that supports PS/2 mouses.
https://www.microsoft.com/en-us/download/details.aspx?id=12772
https://en.wikipedia.org/wiki/IntelliPoint#Supported\_mice
I don't know what happends is you have Windows 7 with both installed Mouse and Keyboard Center and IntelliPoint 8.2, but I have here Win7 64-bit where Microsoft Wireless Laser Mouse 5000 works with IntelliPoint 8.2. Mouse Properties -> Wireless -> Battery Status -> Wireless mouse battery level: Good and Signal Quality -> Wireless mouse signal quality: High
Microsoft Wireless Laser Mouse 5000 is one of the best mouses I have ever used for its great fit to a hand. It also has great quality buttons and it works on more challenging surfaces than many optical mouses.