Sort of, but there is no 5.1-specific certification - you will be certified for vSphere 5.
You will get certified when you've taken the training - it does not matter that the exam was on 5.0 and the training will be on 5.1.
As you're taking the training after the exam, you will need to email certification@vmware.com once you've finished the training to ask them to validate your certification status.
Yes this course would make you eligible for the certification
VCP510 now called VCP5-DCV is based common topics on vSphere 5.0 and 5.1 product
Sort of, but there is no 5.1-specific certification - you will be certified for vSphere 5.
You will get certified when you've taken the training - it does not matter that the exam was on 5.0 and the training will be on 5.1.
As you're taking the training after the exam, you will need to email certification@vmware.com once you've finished the training to ask them to validate your certification status.
Thanks Guys!
See also:
VMware exams and related products version | vInfrastructure Blog
Some updates on the VCP5-DV exam | vInfrastructure Blog