"Sie selbst würden eher eine vier bis fünf vergeben."
I don't know why they translated it to 'or', there's no reason for it since "Vier bis Fünf" has a very distinct meaning. It's a certain grade, as you already know. If you didn't already check, take a look at the "primary and 1st sec" grades: http://en.wikipedia.org/wiki/Grade_(education)#Germany
They left out the half-grades, though. In this case, the order is 4, 4-, 4-5, 5+ and 5 and sometimes they're translated into decimals: 4, 4.25, 4.5, 4.75 and 5.
Another side note: Since school is compulsory, everyone knows this system and thus it is used outside the educational context, too. Stiftung Warentest, which is also widely known (http://en.wikipedia.org/wiki/Stiftung_Warentest), uses the same system – even more detailed, It's often used in other print publications and even spoken language.