Well I'm sure there are a lot of ways to do it but, this is how I would.
Assume the data is in col A, then in col b enter
=if(and(a1>5,a1<10),1,0)
Then all you have to do is sum col b and that will tell you how many numbers are between 5 and 10.
Try:
=COUNTIF(A2:A8,">"&E1)-COUNTIF(A2:A8,">="&E2)
where A2:A8 houses the numbers of interest, E1 the lower limit criterion, and E2 the lower limit criterion.
Note. I assumed an exclusive between. Adjust to what you want COUNTIF to include.
Aladin
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I think Aladin is on the right track, but maybe has a typo. I would use
=COUNTIF(E6:E12,">=5")-COUNTIF(E6:E12,">=10")
(use the >= to include 5 and 10, the > sign for between 5 and 10). You can replace the values 5 and 10 with cell references as aladin did, then type the values (ranges) in those cells
jeff