Cancelling your credit card that is only 5 or 6 months old won't damage your credit score from a credit history perspective (assuming you have other older accounts in good standing). Cancelling it, though, may still damage your score if you'll be losing a significant amount of available credit by doing so. It also depends on how many other accounts you have and how high the limits and your balances are on those.

I would say if they card only has a small limit, you could cancel it without having much affect on your score. If it has a larger limit, consider keeping it open, but just not using it except for very periodically for a small purchase here or there to keep it active (some credit card companies lately are closing accounts due to inactivity).