If the doors work ok then it could be a bad trunk lock actuator. This will require some electrical testing and hands-on inspection.
Use this link to find a good shop near you.
https://repairpal.com/repair-shops
Alex
RepairPal Certified shops can diagnose and repair your 2005 Chrysler Crossfire. They provide transparent pricing with a minimum 12-month or 12,000-mile warranty on repairs and services.