It is indeed a rational number.
Do you know the definition of a rational number?
It is a number which can be exactly obtained by dividing one integer into another integer.
-5.8 can be obtained exactly by dividing -58 by 10. It doesn't matter that -58 is a negative number. It is still a whole number, otherwise known as an integer.
An example of an irrational number (not a rational number) is √2. This number can only be approximated (as 1.414… with as many decimal places as you desire); but it can not be exactly expressed as the ratio of two integers - as a rational number, that is.
Another irrational number is π (pronounced 'pi'). It is approximately 3.14159 - but no number of decimal places will get it exactly; nor will the ratio of any two integers.
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10.01 is a rational number
Rational
Such a product is always irrational - unless the rational number happens to be zero.
The sum of a rational and irrational number must be an irrational number.
rational * irrational = irrational.