How do I restore an iPhone 5 without Factory reset with a forgotten password?

My friend has an iPhone 5 that he forgot the password to, and he wants to recover the password without Factory resetting the device.

Is there a "brute-force" password cracker that can be downloaded, is free, and supports Windows?

Apple added a lot of security layers and mechanisms in the last few years to prevent this from happening, including enforcing longer passwords and preventing access via USB/Lightening port without password entry. So the bar for any brute-force password recovery is rather high (which actually is a good thing). There are some companies out there who claim to be able to access data on a locked iPhone (see The Art of iPhone Acquisition for the challenges associated with that), but this won't reset the password nor recover data in a meaningful manner. These services are also far from free.

So the best approach for your friend is to factory reset their phone and restore the content from backup.