If the rib roast was not wrapped in plastic, and your refrigerator was holding under 40F for the entire time without exception, then congratulations you just dry-aged your rib roast. It should be reasonably safe to eat, but definitely do the smell test. Feel for anything slimy and look for any off-color or furry bits. Take a clean chef knife and trim any discolored, overly dry, or otherwise off-looking pieces from the roast.
If there is no offensive smell or slimy feel to the meat, you should be all good to go. Ideally you would be watching your roast each day while dry-aging, and have it wrapped in something breathable like cheesecloth on a cooling rack for draining extra juices, but give it a try. Just make sure you cook the meat to the recommended temperature (including +10 degrees carryover cooking during resting) before serving.
Sorry, probably not.
See this page (sources from USDA, CDC, FDA) which recommends 3-5 days for raw beef in the refrigerator.
http://www.stilltasty.com/fooditems/index/16496
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If there is no offensive smell or slimy feel to the meat, you should be all good to go. Ideally you would be watching your roast each day while dry-aging, and have it wrapped in something breathable like cheesecloth on a cooling rack for draining extra juices, but give it a try. Just make sure you cook the meat to the recommended temperature (including +10 degrees carryover cooking during resting) before serving.
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See this page (sources from USDA, CDC, FDA) which recommends 3-5 days for raw beef in the refrigerator.
http://www.stilltasty.com/fooditems/index/16496