Not going to go out and say I know specifically.
But I think you should review the following:
AWS QC5 (can be found at AWS.org in the certification drop down menu under education)
http://files.aws.org/certification/CWE/QC5-91.pdfLook specifically at clause 6.3
"6.3 The applicant shall have a valid AWS Certified
Welder ID/Certification card or its equal, or shall pass
a valid AWS Certified Welder test, for the welding
process to be taught."
This really doesn't seem to jive with B5.5
The CWE application package itself references AWS QC5 rather than B5.5
http://files.aws.org/certification/CWE/CWE_Exam_only_pkg.pdf