Hi, I succeed with the wi-fi driver on my VX5-591g. The distro I'm trying is Studio 13.37 v2.4, so probably you are using a different one and you probably might face different issues. Here's what I've done:

1. In the windows' driver manager I found out that the name of the wi-fi driver is Intel® Dual Band Wireless-AC 7265.
2. I went on this link and downloaded one of the Intel® Wireless 7260 files.
3. https://wireless.wiki.kernel.org/en/users/drivers/iwlwifi
4. In "README" there was the following stretch:
   
   "2. INSTALLATION
   
   The iwlwifi driver will look for the file iwlwifi-7265-13.ucode /
   iwlwifi-7265D-13.ucodeusing the kernel's firmware_class infrastructure.
   More information can be found under Documentation/firmware_class in kernel
   source. In order to function correctly, you need to have this support enabled
   in your kernel.  When you configure the kernel, you can find this option in
   the following location:
   
           Device Drivers ->
                   Generic Driver Options ->
                           Userspace firmware loading support
   
   
   You can determine if your kernel currently has firmware loader support
   by looking for the CONFIG_FW_LOADER definition on your kernel's
   .config.
   
   In addition to having the firmware_class support in your kernel, you
   must also have a working udev and uevent infrastructure configured.
   The steps for installing and configuring udev are very
   distribution specific.
   
   Once you have the firmware loader in place (or if you aren't sure and
   you just want to try things to see if it works), you need to install
   the microcode file into the appropriate location.
   
   Where that appropriate location is depends (again) on your system
   distribution.  You can typically find this location by looking in the
   udev scripts of your distro, the default is /lib/firmware.
   
   Installation of the firmware is simply:
   
           % cp iwlwifi-7265-xx.ucode /lib/firmware
           % cp iwlwifi-7265D-xx.ucode /lib/firmware
   (...)"
5. So I went to "Setup Network", then used Puppy Network Wizzard to unload the ethernet module and load the iwlwifi.
6. Then I used Kernel Module Viewer and looked for iwlwifi. When I found it, there was several firmwares under it, and one of them was "iwlwifi-7265-13.ucode". So I went back to the link and downloaded the corresponding file (iwlwifi-7260-ucode-25.30.13.0.tgz).
7. I installed the package, then followed the install instructions on README (using cp in the terminal), and unloaded and reloaded the iwlwifi network module. And it worked like a charm.

Sorry if something isn't clear enough, I'm new to linux, and I don't know the details of how I made it work. I still can't use the touchpad, bluetooth, the sound driver. But I found the touchpad driver (i2c_hid) loaded in Kernel Module Viewer, so I'm going to follow the same logic of looking for the driver name in windows, searching for the linux version to download (after checking the firmware version on Kernel Module Viewer), and then trying to install it. The difference is that now I can list the drivers I need in a file and do the rest of the work without unbooting linux.

Good luck!