Deleting a partition
Don't bother with Mint 19.1, then. 
Just install Mint 18.3 from USB into the free space (or sda5, if its still present - overwriting everything that is there).
sda5 is your combined / (root) and /home partition.
If its convenient, tell the install that you don't want a swap partition - if you are installing into free space, you could choose to have a swap partition.
Make sure to put your boot location as sda - Windows and Mint 18.3 will be detected and a dual boot menu built for them.
If you want to preserve any data files, take a backup first.
Actually, I upgraded Mint 19 to Mint 19.1 today - Mint 18.3 is based upon Ubuntu 16.04 (circa 2016) - so some applications may be a bit dated. Mint 19 is based upon Ubuntu 18.04 (April 2018 ).
Almost certainly Yes - but a point that needs clarifying:-
Have you deleted sda5 outside of the install or is the install doing the delete of sda5 - perhaps in order to split it into
two partitions - a root partition and a swap partition?
If the installer does this then the installer needs to write these changes to the disk partition table, this is quite safe since Windows doesn't look at sda5.
For peace of mind I would run a program before you start the install called gparted (supplied in the menu of the USB boot) which allows you to view your partitions graphically - and optionally delete/resize them. If you make any changes your partition table has to be updated - this is something where "the changes cannot be undone".
I tried an install in a VM of a Mint variation (which uses a blank virtual disk), but got no warnings and the final page before the install started was a summary page:-
So if all you see are references to sda5 (and possibly sda6) everything is fine. References to sda1, sda2 and sda3 are not.
@VileReynard Thank you very much for your detailed reply.... not that I understood most of it ! ( as you know, I am not a linux geek ! ! )... however,... Whilst waiting on your reply... I found some free software that did the job .... AOMEI PARTITION ASSISTANT.
(It says "safely partiltion your hard drives)... and I was very careful on my selection processes.. it took about 5 mins from installing, to getting to the point of Deletion... the program actually does not delete until you finally "approve" it... and then it took about 30 mins to complete..
After it had done it`s stuff... I rebooted... but 
WOE 
WOE 
WOE !..
The hard drive was borked !... would not boot... kept telling me that there was no bootable partition... went through a lot of trauma, and various ideas to get it back, then remembered to GOOGLE FIX MASTER BOOT RECORD... found a linky to
How to fix Windows 7 when it fails to boot https://www.tomshardware.co.uk/win7-windows-7-mbr,news-33163.html
Did the bootrec.exe /FixMbr on the command line.... and IT WORKED>>>>>> 
Yahoo yahoo yahoo All is well in the world....
I have since checked, and the sda5 section has indeed been made free space... now called "Unallocated" .
You have a program called gparted on your USB - you just select the partition to delete and confirm - and it does it safely in about 2 seconds!
From the Mint menu on your USB boot before/after the install choose gparted. It deletes partitions by removing the corresponding entry in the disk partition table. The contents of the partition are left unchanged.
Note that if you run bootrec in future, it will destroy Mint - so you might want to make sure you keep backuups of important data.
@VileReynard OK.. thanks for that... I will bear it in mind... IF .. i need to do the same thing... fortunately, all is well... Just finished updating my backups for pics, videos, and docs I have rebooted Win 7 three times since, and it was good
Not done the install of 18.3 yet... gotta eat some time ! ! .