How to find if a set of objects lies within a given resolution (5 arcsec) on a telescope? I am new to astronomy and I was given the task of finding out if there are objects which can't be resolved by a telescope of resolution 5 arcseconds.

I was given the values of RA and Dec of these objects in degrees. 

   RA              DEC
 201.1999388    27.49294258
 201.2048319    27.49212959
 201.1984702    27.4978016
 201.2025157    27.51610266
 201.1997827    27.51743447 ...etc


How can I find these in the simplest way? Is there any simple formula which can be used to achieve this which is computationally efficient as well?
This would be your best resource. Just note that the variables are expressed in geographical latitude and longitude, and your values are Right Ascension and Declination. Longitude and RA are the same, but Declination is 0 at the equator and is positive toward the north pole, whereas latitude is 0 at the north pole and is positive toward the south pole.

Don't forget to mind your units (it'll probably be in degrees since that's what your RA and Dec are). If you're doing this with a computer, you'll probably want to convert to radians first since most computer trig functions are in radians. Whatever program you use, just be sure to check what units it prefers.

Finally, be sure to convert your separation to arcseconds and you should be all set.