Is -5.8 a rational or irrational number?

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.