There can also be up to three primary partitions and a logical partition, which can hold even more partitions.
First up, I wouldn't go deleting any of those partitions unless you are certain you have a complete working set of recovery disks available.
Second, you should make at least one verified backup of your treasured data before you even contemplate installing any linux OS.
Third, you'll need to a logical partition if you want to get another OS onto that disk. I suspect you don't have one, which would cause that spare space you created to be unavailable in the Mint installer.
To be honest, and I mean no disrespect here, since you had to ask about what to do, I think you might be setting yourself up for failure. Doing what you want to do is not for the feint of heart. You could very well end up with no Windows and no way to recover anything. However, that said, it's your system.
I would recommend that you leave your Windows system alone, check if your laptop can boot from USB external drives, and buy a small, fast external hard disk then install to that. Really, I'd rather see you not install any linux than put you at risk of clobbering everything.
Mint Testing Team & Mint Donor #3606
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