Missing windows boot options

I have tried to install ElementaryOS on my machine, and I have wiped out my boot partition by accident.

I have successfully installed Elementary OS (0.6 Odin, even though it doesn't matter). Now, my grub shows only Elementary, and I cannot get into my Windows.

I have tried the following process (os-prober haven't done anything useful):

Running parted -l yields the following result:

Partition Table: gpt
Disk Flags: 

Number  Start   End    Size    File system  Name                          Flags
 1      1049kB  473MB  472MB   ntfs         Basic data partition          hidden, diag
 3      577MB   593MB  16.8MB               Microsoft reserved partition  msftres
 4      593MB   157GB  157GB   ntfs         Basic data partition          msftdata
 5      157GB   158GB  541MB   ntfs                                       hidden, diag
 2      158GB   158GB  294MB   fat32        NO NAME                       boot, esp
 6      158GB   250GB  91.9GB  ext4         elementary OS

I know that sda2 is the new boot partition I have created. sda4 is the partition of Windows 10, and sda5 is the recovery partition? (I'm really not sure of that).

I have tried to add both sda5 and sda4 to my GRUB by adding the following lines to /etc/grub.d/40_custom:

#!/bin/sh
exec tail -n +3 $0
menuentry "Windows 10 Recovery" --class windows --class os {
    insmod part_msdos   
    insmod ntfs
    set root='(hd0,msdos4)'
    search --no-floppy --fs-uuid --set=root EE92464E92461C09
    chainloader +1
}

menuentry "Windows 10" --class windows --class os {
    insmod part_msdos   
    insmod ntfs
    set root='(hd0,msdos4)'
    search --no-floppy --fs-uuid --set=root 28981AAB981A7790
    chainloader +1
}

After using:

> sudo blkid /dev/sda4
/dev/sda4: UUID="28981AAB981A7790" TYPE="ntfs" PARTLABEL="Basic data partition" PARTUUID="09b51487-4e98-458a-9a50-0a4470e4f844"

> sudo blkid /dev/sda5
/dev/sda5: UUID="EE92464E92461C09" TYPE="ntfs" PARTUUID="6805dc0a-c750-4ef6-a06d-f41ad4ab3f2a"

And of course, I ran sudo update-grub.

However, I get an error: "Invalid EFI file path" when trying to boot from these new entries.

Also, mounting the new boot partition and running ls yields:

EFI
-> BOOT
-> ubuntu

Meaning, I don't have the windows (and windows recovery) boot entries.

I really don't want to reinstall my windows and Elementary again. However, I have no idea how to fix this.

+1 asks the 'chainloader' command to load the 1st sector of the partition. But your computer uses EFI firmware – it doesn't use boot sectors, so "+1" will do nothing useful at all. Instead, the parameter to the 'chainloader' command has to be a path to an *.efi executable file containing the bootloader.

Windows always installs its bootloader at \EFI\Microsoft\Boot\bootmgfw.efi (relative to the root of the EFI system partition, not the main Windows partition, so you shouldn't be using "set root" either).

(The "part_msdos" bit is incorrect too, as your disk has a GPT partition table. Basically the entire custom menu item is specific to BIOS systems and does not apply to your EFI machine.)

Since you've deleted the old partition – boot from a Windows install CD (or USB stick), hit Shift+F10 to open a console window, then use the bcdboot c:\windows command to reinstall the Windows bootloader – it will copy all necessary files, rebuild the "BCD" configuration file, and add an EFI boot entry.

(If creating the Windows USB stick using Rufus, make sure you select the UEFI mode, as it only does one or the other.)