How long will it take if I file I-130 and I-485 for my mother if she had a 5 year multiple visa for US?

Once your file the I-485, she is protected in remaining in the US. It is currently taking about 4- 6 months for the I-485.

I begin by answering your last question first. If you are a US citizen, then, your mother is considered an immediate relative of a US citizen [you]. Immediate relatives can and remain eligible to adjust status even if they remain in the US long after their visas have expired. From your query, it appears you initially filed your mother's I-130 petition separately when instead, you should have concurrently filed both applications at the same time. If you only filed the I-130 application, then, you may have to wait to file the I-485 [green card] application because, you may not file her green card until after her I-130 petition has been approved. You will have to get the I-130 approved before you can proceed to her I-485 adjudication. Further, if you filed her I-130 petition so soon after her arrival as a tourist, CIS might consider that she misrepresented the real reason for her coming into US having arrived as a tourist, only to then file application for permanent resident. Please hire an attorney, I urge you.

USCIS is currently taking about 4-6 months to adjudicate an I-485 application that is based on an I-130 petition filed by a U.S. citizen son or daughter. Under U.S. immigration law, your mother is considered an immediate relative of a U.S. citizen. Thus, she can apply for adjustment of status at anytime as long as she entered the U.S. with inspection, even after her visa or authorized stay expires.

If you are a U.S. citizen 21 years old or older petitioning for your parent, then any unlawful presence that she might accumulate after her visa expires will be forgiven. The reason for this is because she is considered an immediate relative. It takes about 6 months to process these applications. You should know that if you are just a legal permanent resident then you are not able to sponsor a parent, only U.S. citizens 21 years old or older can sponsor parents.

Assuming you have done the paperwork correctly, and assuming they match-up your two separate application filings, the government is often taking 10-16 months on these cases.