The OP did not ever have the first choice, to install alongside Windows. Revisit the old Topic
That's exactly what I was referring to in Post #8 & why the jargos just needs to create recovery media, image that partition separate (for fast future restore if desired) & then the entire drive. Once that's done, delete the Recovery partition & Linux Mint (or any Ubuntu based Linux) will install like a charm. As far as the 'old Topic' goes, that's why this one was created.
The most time will be spent in preparation (steps above), the OS install, as Nick implied, is a walk in the park, once the needed steps are taken to free a partition. No one needs to know all of the technical jumbo to perform this task, except for the question below.
How many more times does it need to be repeated that there's a limit of 4 Primary partitions per drive? Linux cannot just step in, break the rules & overcome this, MBR is a standard that has zilch to do with Microsoft or Linux, rather engineers who were tasked to create a better way for the times, of which is rapidly changing to the newer adopted one (in 2012 after being a 64 bit standard for 7 years prior). If it were on a GPT based drive (like on all computers that ships with Windows 8 or above), it wouldn't matter, yet it's not. If one has created their Recovery Media set, in essence, there's no need for a Recovery partition, other than it reloads the OS faster than DVD's. Flash drives, especially the USB 3.0 type, are too unreliable for this task, you are forced to choose the 'right one'. DVD's are slower yet more stable, have never had a DVD based recovery set to not work.
Microsoft simply took the work of others & implemented the way they wanted, 3rd party computer engineers also came up with Secure Boot, not as a Microsoft project, but it was they who took the technology & shaped it the way they wanted it to be. It's usually 3rd parties unrelated to many technologies who creates these & passes off to the highest bidder & this isn't limited to computers.
Get rid of that Recovery partition & you're set for a Linux dual boot. Once you've done that, you can follow the instructions Nick linked in Post #13, this is assuming 3 Primaries & is indeed correct. Very few clings onto these partitions on a MBR drive anymore, it ties the user's hands behind their back as to what one can do. Plus on SSD's, it's usually dead weight, as the 'hook' to boot the partition is broken. Even if it did boot, most OEM's expects to 'see' a drive at least as large as the original installed for a successful recovery.
Linux happily runs on Logical partitions, so no issue there, once installed.
Either that, or install another drive. If a notebook, there are 9.5mm & 12.7mm optical bay to HDD/SSD adapters to install a 2nd drive in most any notebook, I have three of these & need a 9.5mm one for my Samsung, identifying which one is the tricky part, my others simply accepted universal 12.7mm models for less than $10. The optical drive can still be used with a $5 USB 2.0 or $7 USB 3.0 adapter & there's enclosures for these as well for portability.
If a tower or desktop PC, simply install a 2nd HDD. If you're that attached to your Recovery partition, that's the only other alternative I can suggest.
While I realize it's not the consumers fault that these OEM's includes so many partitions, when we want to dual boot another OS (even Windows), we do what we have to in order to get what we want done.
You're not helping, Nick. The article states, amongst other differences, at step 5
And neither are you, Wiz. Otherwise you should know the same as what I've pointed out in two posts in this Topic. With the experience you have, you should know the simple rules of MBR partitioning & the obvious one not needed. Recovery, if the media has been created & the partition imaged for a 'just in case' situation. Then jargos can defrag the drive good & shrink the needed space for a Linux install. How much to shrink depends on his needs. At a minimum, 20-25GB for root, a 1024MiB Swap & whatever needed for /home. Some users may find a /home of 30GiB to be plenty, while others may want 100GiB.
I guess in another 5-6 years time when more & more of these MBR based computers are dropping like flies, then folks will see & appreciate the GPT standard. How much trouble was it to setup a dual boot on your wife's computer? Probably very little. Users with 64 bit systems can do the same now, if only they'll take the time to perform a clean install on an initialized GPT HDD & no, UEFI isn't needed for this. That technology didn't exist in the Windows Server 2003 64 bit & XP 64 bit days, yet both would install perfectly on GPT drives.