Question

nitrogen gas occupies 6.5L at 27 C and 5 atm pressure. What will the volume be at -100 C and the same pressure

Answer 1

ok for this kind of problems you should always use pV=nRT and in this case you have same amount of gass but different variables so:
n1=n2 (1and 2 are states of gas at given pressure, temperature and volume)
n=pV/RT
p1V1/T1=p2V2/T2
cause R is constant it strikes out, now you have that pressure is the same so:
V1/T1=V2/T2
so V2 or volume at different temperature is:
V2= V1 T2/T1

Answer 2

and don't forget to convert those temperatures to Kelvin