mate i'll start this post before my midday because then it's beer o'clock. hope it is not TL;DR - too long, don't read

, but i want to be sure you are aware of your options. a little explanation first.
..so if I can't get Linux installed without erasing the disk,..
you
can - we can work voodoo
having windows 10, you likely have a uefi computer, which can be switched between BIOS (Legacy) and UEFI. if you are limited in apparent partitions it is because it is likely that your 640 GB drive is in MBR (Master Boot Record) format aka MSDOS. the newer alternative is GPT.
limitations on the MBR system include but are not limited to:
- support for a single drive cutting off at 2 TB; drives larger than 2 TB have to be partitioned to be used
- support for a single file to a size of 4 GB, larger file size unsupported
- on one drive, a maximum of four (4) primary partitions or three (3) primary partitions and one (1) extended partition
that last point is known as "the 4 partition rule", a limitation imposed by M$, not Linux, but affects us.
the good news is that if only 3 partitions are in use on your rig, and there is unallocated space, you can use linux to create a 4th, Extended partition beside them, which can then be used to create Logical partitions to house Linux.
actually, i'll split this post and leave you with some questions.
- i take it you are familiar with the windows disk management tool, unless you used 3rd-party to resize the drive partitions, you could show us a screenshot of your partitioning setup
- ...using the windows snipping tool found in your Start menu - its default shot is to .png which is fine
- do you have an external recovery plan in place, should windows go kaput?
with the screenshot you need to show us both the textual lines and also the graphical representation below that, drag your window handles if need be so as to capture all the info
you can either use the paperclip - attach files - to upload, if so, choose fullsize over thumbnail, or use an image hosting provider such as imgur or photobucket, to place them here - see my thread here
https://linux.org/threads/posting-screenshots-at-this-site-read-this-for-easy-way.21722/
... crap sound, will fix that one decade.
cheers
wizard