is .0000000500050005 an irrational number

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Unless it terminates right there on the last 5 you typed, yes, it is an irrational number. Irrational numbers are numbers that don't terminate nor repeat to the right of the decimal point. Since you had 7 zeroes and then one 5 in the first numbers, then 3 zeroes and then one 5 in the next few numbers, it is not repeating. You did not mention that it does not terminate, so I asked you if it terminates. If it terminates, it is a rational number. If it does not terminate, however, it is an irrational number. Basically, you just need to know the definition of "irrational number."