Actually, "since" and "ago" can be used together, and very logically.
"The old man has been in the hospital since 5 months ago" is correct. If you start from today, February 3, it means that the old man began to be in the hospital last September. That was the starting date of his hospitalization (since...).
"Ago" states the period of time that has passed since then. In this case, it's five months.
You are correct that "since" tells the starting date of the period. We could say, "The old man has been in the hospital since September."
- The old man has been in the hospital for 5
This is your sentence, and it is correct. It means essentially the same as, "The old man has been in the hospital since 5 months ago."
- The old man was in the hospital 5 months ago .
It's true that you can say the sentence above. But, it means that the old man was in the hospital 5 months ago, but he isn't anymore.
Here are some examples from Google of "has been someplace since a time ago":
"¢ ... and climate was as warm as it has been recently. Since 1900 years ago, the shelf was, however, continuously present until it disappeared in 1995 (14). ...http://www.sciencemag.org/cgi/content/full/293/5536/1777
"¢ This flow has been going on since 15000 years ago (at least) and continuing into the present. As part of this emphasis, BELA has been designated as a core ...http://www.nps.gov/akso/akarc/cr_bela.htm
"¢ Ayurveda has been a vogue since 5000 years ago. Our Vedas have been repeated references to the efficacy of Ayurveda as a science of healthy life. http://ezinearticles.com
"¢ This has been the case since 5000 years ago, when the Sumerians started to press a stylus into clay forming their cuneiform characters in the first written ...http://jodi.tamu.edu/Articles/v06/i01/Hillesund/
"¢ What needs to be done also has been well known since 20 years ago, when a nonpartisan report by a cross-party group of big-city mayors unanimously agreed on ...http://www.project-syndicate.org/commentary/rocard10
"¢ My Dad has been in Australia since several years ago,he took me a sheep toy and a red hat. Have a nice trip.
. Posted by: lu on September 30, 2006 01:12 PM ...http://home.wangjianshuo.com / archives /20060929_jian_shuo_in_au...