Sorry, but without a working touchscreen, the phone can't be unlocked manually.
You'll have to get it serviced by visiting an Authorized Apple Service Provider or Apple Store. You can also contact Apple Support and request a screen repair:
iPhone - Contact Support - Apple Support
Screen repair service pricing
Repair and replacement costs depend on your iPhone model and your AppleCare product coverage. Apple will run a diagnostic test to determine whether your iPhone has experienced additional damage. If it has, or if it needs other repairs, you may need to pay an out-of-warranty service fee. Accidental damage isn't covered under the Apple One Year Limited Warranty.
Model |
Screen repair cost |
iPhone 6 |
$109 |
iPhone 6 Plus, iPhone 5s, iPhone 5c, iPhone 5 |
$129 |
Plus a $6.95 shipping fee, if required. Fees are in USD and exclude local tax. Pricing is for service through Apple. The final service fee we charge will be determined during testing. Pricing and terms vary for service through an Apple Authorized Service Provider.
copied from Service Answer Center - iPhone