Your configuration is very strange. According to the Boot Info Script output, the only NTFS volume on your system is /dev/sda5, which is a logical partition. The Boot Info Script has identified a winload.exe boot file on that volume, so it looks at least a bit like a Windows boot partition. The puzzling thing is that Windows boot partitions are almost never logical partitions; Windows will only install to primary partitions, and getting it to boot from a logical partition requires jumping through several hoops. (I'm not familiar with the details of those hoops, either.)
So the question is: How did it wind up like this? The Mint installer shouldn't have done it, and AFAIK the Mint installer doesn't even ship with software that
could have done it. Thus, I suspect that you did something unusual to set it up like this -- maybe you used some unusual partitioning software to prepare your hard disk or you installed in an unusual way.
My first thought about a solution is to use
FixParts to convert /dev/sda5 from a logical partition into a primary partition. Once this is done, you should be able to reboot into Linux and type "sudo update-grub" to create a fresh GRUB configuration file that will, with any luck, include your newly-restored Windows partition.
That said, I can't guarantee that this will work; it could be that your Windows installation has been damaged by whatever set up your odd partitions. It could also be that your original configuration was unusual in some way that's relevant to finding a solution -- for instance, if you set Windows up to boot from a logical partition or if you originally used a GUID Partition Table (GPT) but converted to MBR form. Thus, if you have any information about unusual partitioning tools you may have used, I recommend you post that information before using FixParts to convert /dev/sda5 into a primary partition, lest that action be a waste of time or even do more harm.