Inspiron N5110, HD fail, how to reinstall Windows?

Yes, you can install Windows 10 on that laptop.

I suggest that you replace the hard drive with an SSD, rather than buying a new hard drive. An SSD will make that old system much more responsive. And note that if you have only 4 GB of RAM, Windows 10 will be rather frustratingly slow. If you have spare RAM, it will work much better with 8 GB RAM and an SSD.

Is the Windows 7 Product Key known? It may be printed on a sticker on the laptop's bottom cover or in the battery compartment.

If you cannot locate the Windows 7 Product Key then there is another option. If the drive is still somewhat readable, you could connect it to an external USB interface or enclosure and on another computer use a tool such as Nirsoft ProduKey or Lazesoft Windows Key Finder to find the Product Key. I've used Nirsoft ProduKey on several laptops.

On another computer, go to Dell Support page for Inspiron 15R N5110 to download chipset drivers, graphics drivers, etc. to an external drive or flash drive.

Here are my detailed steps to perform a clean install of Windows 10. And, here's another description of the install process, from a Microsoft MVP. At some point in the process the installer will ask you for a Product Key, at which point you should be able to enter the Windows 7 Product Key.

If you cannot find the Windows 7 Product Key, you can buy a Windows 7 or Windows 10 licence from many on-line sources for fairly cheap prices.

I suggest that you keep Internet disconnected for the first part of the Windows installation process. Once you install Windows, next thing to do is to install the chipset drivers that you downloaded earlier. Then you can connect to the Internet and run Windows Update, which may automatically install most of the other drivers that you need. After several rounds of running Windows Update and rebooting, you can then manually install any needed drivers that you obtained from Dell Support page for Inspiron 15R N5110.

How to Install Dell Drivers in the Correct Order. 

Note: that system will never be fast. SSD and 8 GB RAM will improve it, but it's still an old budget laptop. If you don't have spare RAM available, consider how much you will spend on this old laptop versus buying a used laptop of a newer model.

Whenever touching components or working inside a computer, wear a grounded wrist strap, also called anti-static wrist strap, ESD wrist strap, or ground bracelet. It's a cheap and sensible precaution. Rest the laptop on an anti-static mat or at least a reasonable alternative such as corrugated cardboard. (Repeatedly touching a metal case part is not sufficient mitigation with modern components.)