You can go about pulling the data in one of two ways.
Pull the drive and attach it to another computer using a USB adapter to pull the data. If the recovery computer has USB 3 ports then consider a USB 3.0 adapter
otherwise a USB 2 will also work.
Boot a live linux distro like Parted Magic and copy the data to a USB external drive using the below guide. Burn the iso to a CD on any Windows 7 or later computer by right clicking and selecting burn disk image. Because this is a Windows 10 disk with most likely has fast startup enabled Parted Magic will mount the drive as read only. Note before you start the copy operation with Parted Magic you can click Disk Health on the desktop and look under the Attributes tab for any red rows. If the drive icon itself is red I would recommend consulting a professional data recovery service depending on how important your data is but this is not inexpensive.
I would start with the most important data first as the process of reading the drive could result in a complete failure. Don't run chkdisk on the drive. If you have a empty drive with the same or larger capacity you could do a sector by sector clone and then work on the cloned image and not the failing drive. The process of cloning the drive could cause the drive to fail.
If Parted Magic does not boot then use Mint Cinnamon. Burn the iso to a DVD. Do no input anything until you are at the Mint desktop. Click Computer on the desktop. Your HDD will be shown in the lower left pane. Clicking on it will mount the drive and a file manager window should open showing your files. Attach a USB external drive. A USB icon will appear in the left pane. Click on it. You can then copy, not move, and paste your files into the USB file manager window.