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Yes,  \sqrt{5} is a terminating decimal. 

And I am saying decimal, because I figured out that's what you really wanted to ask about. There aren't things like terminating digits, there are though - terminating decimals

You see, a terminating decimal is such a decimal which has a finitive number of digits coming after the decimal point. For example: 
              0.25 - 2 digits (2 is finitive)
          0.7354 - 4 digits (4 is finitive)
                0.4 - 1 digit (1 is finitive)
            0.996 - 3 digits (3 is finitive)

What kind of decimals are not terminating decimals then? There are two types of them:
    1. decimals who will have an indefinitely repeating sequence of digits after the decimal point, like \frac{1}{3}=0.33333333... 
    2. irrational numbers, like

Bottom line, if a decimal has a finitive, natural number of digits coming after the decimal point, it is a
terminating decimal.

1 5 1
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