GRUB problems, not showing windows 10

Hello everybody

(i read already the other posts of people facing my same issue, but i couldn’t resolve in that ways…)

i just installed Manjaro on my Office Desktop.

i have to use several windows programs on it, so i decided to have both OS together.

i dont have UEFI system, just BIOS on a Lenovo Desktop PC.

Grub does not show the windows 10 option at boot

i will post few informations regarding my system.

> [engine@Luminosity-Engine ~]$ lsblk

sr0 11:0 1 1024M 0 rom
nvme0n1 259:0 0 238,5G 0 disk
├─nvme0n1p1 259:1 0 529M 0 part
├─nvme0n1p2 259:2 0 100M 0 part
├─nvme0n1p3 259:3 0 16M 0 part
├─nvme0n1p4 259:4 0 68,5G 0 part /run/media/engine/Win10Pro_64bit
└─nvme0n1p5 259:5 0 169,3G 0 part /
[engine@Luminosity-Engine ~]$

[engine@Luminosity-Engine ~]$ inxi -Fazy
  Kernel: 5.9.16-1-MANJARO x86_64 bits: 64 compiler: gcc v: 10.2.1 
  parameters: BOOT_IMAGE=/boot/vmlinuz-5.9-x86_64 
  root=UUID=5e871870-16d1-4265-9e95-bf3a714bf417 ro quiet apparmor=1 
  security=apparmor udev.log_priority=3 
  Desktop: Xfce 4.16.0 tk: Gtk 3.24.24 info: xfce4-panel wm: xfwm4 
  dm: LightDM 1.30.0 Distro: Manjaro Linux 
  Type: Desktop System: LENOVO product: 10M70007IX v: ThinkCentre M710s 
  serial: <filter> Chassis: type: 3 serial: <filter> 
  Mobo: LENOVO model: 3102 v: SDK0J40697 WIN 3305076253216 serial: <filter> 
  UEFI [Legacy]: LENOVO v: M16KT65A date: 06/11/2020 
  Info: Quad Core model: Intel Core i5-7400 bits: 64 type: MCP arch: Kaby Lake 
  family: 6 model-id: 9E (158) stepping: 9 microcode: DE L2 cache: 6 MiB 
  flags: avx avx2 lm nx pae sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx 
  bogomips: 24008 
  Speed: 1100 MHz min/max: 800/3500 MHz Core speeds (MHz): 1: 1100 2: 1101 
  3: 1101 4: 1100 
  Vulnerabilities: Type: itlb_multihit status: KVM: VMX disabled 
  Type: l1tf 
  mitigation: PTE Inversion; VMX: conditional cache flushes, SMT disabled 
  Type: mds mitigation: Clear CPU buffers; SMT disabled 
  Type: meltdown mitigation: PTI 
  Type: spec_store_bypass 
  mitigation: Speculative Store Bypass disabled via prctl and seccomp 
  Type: spectre_v1 
  mitigation: usercopy/swapgs barriers and __user pointer sanitization 
  Type: spectre_v2 mitigation: Full generic retpoline, IBPB: conditional, 
  IBRS_FW, STIBP: disabled, RSB filling 
  Type: srbds mitigation: Microcode 
  Type: tsx_async_abort status: Not affected 
  Device-1: Intel HD Graphics 630 vendor: Lenovo driver: i915 v: kernel 
  bus ID: 00:02.0 chip ID: 8086:5912 class ID: 0300 
  Display: x11 server: X.Org 1.20.10 driver: loaded: intel 
  unloaded: modesetting alternate: fbdev,vesa display ID: :0.0 screens: 1 
  Screen-1: 0 s-res: 1920x1080 s-dpi: 96 s-size: 508x285mm (20.0x11.2") 
  s-diag: 582mm (22.9") 
  Monitor-1: DP1 res: 1920x1080 dpi: 102 size: 480x270mm (18.9x10.6") 
  diag: 551mm (21.7") 
  OpenGL: renderer: Mesa Intel HD Graphics 630 (KBL GT2) v: 4.6 Mesa 20.3.4 
  direct render: Yes 
  Device-1: Intel 200 Series PCH HD Audio vendor: Lenovo driver: snd_hda_intel 
  v: kernel bus ID: 00:1f.3 chip ID: 8086:a2f0 class ID: 0403 
  Sound Server: ALSA v: k5.9.16-1-MANJARO 
  Device-1: Realtek RTL8111/8168/8411 PCI Express Gigabit Ethernet 
  vendor: Lenovo driver: r8169 v: kernel port: e000 bus ID: 02:00.0 
  chip ID: 10ec:8168 class ID: 0200 
  IF: enp2s0 state: up speed: 1000 Mbps duplex: full mac: <filter> 
  Local Storage: total: 238.47 GiB used: 44.62 GiB (18.7%) 
  SMART Message: Required tool smartctl not installed. Check --recommends 
  ID-1: /dev/nvme0n1 maj-min: 259:0 vendor: Samsung model: MZVLW256HEHP-000L7 
  size: 238.47 GiB block size: physical: 512 B logical: 512 B speed: 31.6 Gb/s 
  lanes: 4 serial: <filter> rev: 5L7QCXB7 temp: 26.9 C 
  ID-1: / raw size: 169.31 GiB size: 165.65 GiB (97.84%) used: 8.24 GiB (5.0%) 
  fs: ext4 dev: /dev/nvme0n1p5 maj-min: 259:5 
  Alert: No Swap data was found. 
  System Temperatures: cpu: 29.8 C mobo: 27.8 C 
  Fan Speeds (RPM): N/A 
  Processes: 191 Uptime: 21m wakeups: 0 Memory: 7.68 GiB 
  used: 1.78 GiB (23.1%) Init: systemd v: 247 Compilers: gcc: N/A Packages: 
  pacman: 1125 lib: 369 flatpak: 0 Shell: Bash v: 5.1.0 
  running in: xfce4-terminal inxi: 3.3.00 
[engine@Luminosity-Engine ~]$ 

can somebody help me?

thank you