How to unlock my iphone 5 when i forgot the password and i want to restart it with computer but my home button is broken

If a button or switch isn't working on your iPhone or iPad, click here -> If a button or switch isn't working on your iPhone or iPad - Apple Support

If that doesn't help then get the phone repaired.

For the iPhone Service Answer Center click here --> Choose Your Country or Region - Apple Support

Select your country.

For a cost estimate:

- Scroll down to "Get an estimate"

- Enter the service required

- Enter the iPhone model you have

- Enter the version of that model

- Click "Get estimate"

For instructions on how to get your iPhone, iPad, or iPod touch ready for service click here --> Get your iPhone, iPad, or iPod touch ready for service - Apple Support

- "To protect your information and save time, follow these steps before you get service for your device."