The five-character word is a convention, not a count of real words. It exists so that scores stay comparable between a test full of short words and one full of long ones, and between languages with different average word lengths.
Two numbers usually get called WPM. Gross WPM counts everything you typed. Net WPM subtracts a penalty for errors, which is why the same run can score 75 on one site and 62 on another. When you compare your speed against a figure you read somewhere, check which one it is before drawing conclusions.
WPM also depends heavily on the text. Common English prose types much faster than code, numbers, or unfamiliar vocabulary, so a single number without its source text says less than it looks like it does.