How to add Windows 10 to grub boot loader?

1. I have installed Windows 10
2. I have installed Linux Mint Silvia and I have chosen a device for boot loader installation - sda.
3. There is not Windows 10 in grub menu when the system starts
4. I have booted via Linux Mint live USB.
5. I Do step by step
6. But it still no Windows 10 in grub menu
7. I have booted via live windows 10 USB.
8. With restoration tools, I have chosen the command line
9. I have fixed Mbr by console command bootrec /FixMbr
10. Ok, windows 10 is loading by there is no Grub.
11. I have repeated steps 4 and 5
12. There is no result

Also, I have tried to change grub config with this answer - But in this case, There is Windows 10 - but when I chose - I will recursively going to grub

And with this answer I have an error message when chose Windows 10 - There is no bootmgr directory

Thanks @Kinnectus for help

Also, I have tried

sudo os-prober

And getting

/dev/sda1:FreeDOS:FreeDOS:chain
/dev/sda2:FreeDOS:FreeDOS1:chain

And then I have tried

sudo update-grub

And getting

Generating grub configuration file ...
Found linux image: /boot/vmlinuz-4.10.0-38-generic
Found initrd image: /boot/initrd.img-4.10.0-38-generic
Found memtest86+ image: /boot/memtest86+.elf
Found memtest86+ image: /boot/memtest86+.bin
Found FreeDOS on /dev/sda1
Found FreeDOS on /dev/sda2
done

Unfortunately - there is not Windows 10 in grub menu

Also, I have fdisk output.

Device Boot Start End Sectors Size Id Type
/dev/sda1 2048 16779263 16777216 8G c W95 FAT32 (LBA)
/dev/sda2 * 16779264 33556479 16777216 8G c W95 FAT32 (LBA)
/dev/sda3 33556480 770219115 736662636 351,3G 7 HPFS/NTFS/exFAT
/dev/sda4 770220030 976771071 206551042 98,5G 5 Extended
/dev/sda5 770220032 976771071 206551040 98,5G 83 Linux
Partition 4 does not start on physical sector boundary.

There is an issue. Maybe the problem is with this issue?

Please, help me, I am stucking with this a whole day. I completely have no idea, what am I doing wrong.

2 Answers

1. Boot to your Linux
2. Open a Terminal window
3. Type: sudo os-prober
4. If the results identify a Windows 10 install, type sudo update-grub which will update the GRUB entries and add it
5. Reboot your computer and test to see if Windows 10 is a new option to select.
6. End of instruction.

Try Boot-Repair tool. It seems easy and working in most cases

See details in answer