If a blood alcohol test is taken, but the sample is not tested for 5 weeks, is the test still accurate? Can the sample deteriorate?

Labs and Liability. If a lab is testing a sample and reporting a result then it has significant liability if the sample is not appropriate for testing. I would bet that the sample tested is accurate if the lab is willing to report the results.
How was the sample. Preserved? Five weeks is generally too long to store whole blood and it will deteriorate. Was it for medical testing or for legal reasons? If it was legal reasons your lawyer should be able to help.