My Galaxy S5 has same problem. Searching for an answer, Found this video.
search youtube for
"Samsung Galaxy S4: How to Make Call When Phone is Locked With Bluetooth Headset " by ITJungles
I cannot post links, sorry.
I am heading out to the car to try it now. I'll edit post and let you know if it worked.
-john
Edit:
It Worked!
Been having this problem since I got the S5, and this fixed it.
Summary:
Could not make outgoing calls with my vehicle bluetooth when S5 screen locked and off.
Solution:
1. Open Phone dialer
2.Click on 3 dots for "Settings"
3. choose "Call"
4. choose "Call Accessories"
5. choose "Outgoing call conditions"
6 choose "Even when screen is locked"
DONE!
-john