not ideal, but you have to be able to function as well.
definitely discuss other options with your OB and consider seeing a chiropractor as well (mine has been a lifesaver...)
Being that you are only 5 weeks, I would not worry about it too much. Especially if the hospital knew you were pregnant. They are very careful about what they give pregnant women these days. I would think it would be an issue with long term use, but I am certain your OB can help work through this with you. You certainly cannot be in constant pain, that's no good for you, and therefor no good for baby. But it most definately is something to discuss with your OB, particularly if your back issue is an ongoing issue. The pain can be managed in a safe way.
Congrats on your pregnancy and best wishes!!