There are five classical planets (not counting Earth) : Mercury, Venus, Mars, Jupiter and Saturn. These five are all bright enough (or more) to be seen with the naked eye and they've been known since before we have written records. To at least the Sumerians, who had names for them in ~3,500 BCE. It's likely that we get the association of the planets with mythlogical gods from the Sumerians.
It's actually not hard to distinguish these planets from the stars, if you observe the night sky carefully. Apart from the fact that they're all quite bright (and therefore noticeable) they exhibit one property that the stars do not : they move.
As the Earth and the planets orbit around the Sun you can observe them shift against the background stars. Even over the course of just a few days for closer planets. This arises since when compared to the distant stars the viewing angle to the (relatively) nearby planets changes noticeably. Over several months to a year the planets will appear to be completely different areas of the sky as the planet itself moves in its orbit.
The word planet is itself derived from the Greek word planētēs. Meaning wanderer.
Couple of technical points :
The 6th planet to be discovered was Uranus in 1781 by William Herschel. It had likely been observed before the invention of the telescope, but because it is quite dim (and thus unremarkable) and it's apparent motion is quite slight it was not recognized as a planet. So this is the exception.
The stars do move. But their motion is so imperceptible that it took until 1718 for Edmund Halley to measure it for the first time.
Neptune is not visible to the naked eye, but it's possible Galileo came close to discovering it during his observations of Jupiter. The two were close together in the night sky at the time and his drawings have a star plotted where Neptune would have been. There is some evidence that Galileo was aware that this star had moved.