I am assuming the one on the left is the desktop. Yeah, that is pretty bad. The laptop doesn't look too bad. I am assuming the 11 GB partition is a factory recovery partition. For now, I wouldn't do a clean install unless you are absolutely sure you are sticking with WIndows 10. You have 30 days to decide if you want to revert back to your old OS if you have the Windows.Old folder intact and before doing a clean install I would do a complete disk image using Macrium in case the Windows 10 clean install went bad.
If I was partitioning you would have the EFI partition, the hidden System Reserved Partition, the Windows partition, and any data partition and finally the 450MB partition. That would be four in DIsk Management, not seven. After WIndows 10 the factory restore partition would be useless if you plan on sticking with Windows 10 as you would be create a Macrium Disk image after doing a fresh install. This would take the place of a factory restore partition.
I am not too familiar with the 450MB WinRE partition. I believe this is used when you need to troubleshoot Windows (see below image). Windows 10 will add this on a clean install but you should not need two. The reason you have two is because WIndows 8.1 added one and Windows 10 added the other.