Is there a more distant object than NGC 4889 (Caldwell 35) that I can see with my 5-inch reflector?
Yes, by a factor of 7! Think quasars. NGC 4889 is a member of the Coma Galaxy Cluster, which lies about 300 million light-years away. But the quasar 3C 273 is 2 billion light-years away. While a little fainter than NGC 4889, it should be barely visible in your 5-inch if you have a dark sky. If you can spot 3C 273, you’re seeing light that is older than multicellular life on Earth. This was the second quasar discovered, and it’s still the brightest known. Looking exactly like a star of about magnitude 12.8, it lies in Virgo at right ascension 12h 29.1m, declination +2° 03' (equinox 2000.0), about 5° northwest of the beautiful double star Gamma Virginis. A detailed finder chart for 3C 273 appears in Burnham’s Celestial Handbook, Vol. 3.
— Alan M. MacRobert