Can I claim my sister-in-law's $5,000 bank account with a small estate affidavit, or do I have to be a blood relative?

You are not her heir. Without a will you have no right to present a Small Estate Affidavit to get the account.

If your sister-in-law did without a spouse, had no children, and her parents pre-deceased her, then her siblings would be her heirs under the statutes on Descent and Distribution. If your husband was alive at her death and was her only sibling then he would be her sole heir. He could file a claim for the asset using a small estate affidavit, assuming no probate was opened for his sister. You can only use a small estate affidavit if the assets are less than $100,000. What was the value of her assets when she died. What happened to her assets then? If an estate was opened then it may have to be reopened now. If no estate was opened for her then you would have to open an estate for your husband to file a claim on his behalf. You should consult with an attorney.