They only knew of five planets - the ones which are easy to see with the unaided eye.

That's Venus and Mercury, the two innermost planets, closer to the sun than Earth, which are sometimes visible as bright stars at dawn or dusk, and in the early evening or in the morning before the sun rises.

Then Mars, Jupiter, and Saturn which are further away from the sun than us and can be seen at any time of night, depending where they are in their orbit relative to Earth.

Earth of course is also a planet but most of the ancient astronomers didn't know that, so didn't count Earth in their list of planets. Except for Aristarchus in the third century BC. Heliocentrism

That leaves Uranus, Neptune and Pluto, and then there are the largest asteroids, or "minor planets" Ceres and Vesta, which you don't mention in the question, but could potentially have been seen by ancient astronomers.

Uranus is a naked eye object (just) to unaided eye, but it's a challenge, as it just looks like one of the faintest stars.  You could theoretically discover that it was a planet with naked eye as a careful, patient, thorough observer. To do that, you'd need to plot all the stars in the sky right down to the very faintest you can see in excellent seeing conditions, and then replot them, and notice that one of the very faintest stars has changed position since the previous night.  But it's so faint, it's more likely you'd just conclude you made a mistake first time around, or that you missed it last time you looked.

And actually, it may have been plotted by Hipparchos, in his star catalogue about 128 BC. WAS URANUS OBSERVED BY HIPPARCHUS?

It was observed many times before its final discovery by Hershel in 1681, and even given a star number, when it was in the constellation Taurus, catalogued by the astronomer royal John Flamsteed as 34 Tauri. For more about this, Patrick Moore's Data Book of Astronomy and Uranus

But nobody realized it was a planet until Hershel turned his telescope to it, on March 13, 1781. Hershel was a noted astronomer of his time, who made particularly good telescope mirrors  (and large aperture for his day) for observing the stars clearly. He  observed it as a disk not just a point of light.

Then Neptune was discovered in the nineteenth century, through a telescopic search based on predictions from perturbations of the orbit of Uranus.

Then in the nineteenth century they found Vesta and Ceres, largest of the asteroids and other asteroids.

Vesta is sometimes bright enough to be seen with the naked eye as well, though never discovered in ancient times. Ceres also might also occasionally be seen with the naked eye by a keen eyed experienced observer from a very dark site.

If You Can Find Mars, You Can Spot Ceres And Vesta Too – Try It!

The Position of Vesta and Ceres in the Night Sky, 2014

Neptune is usually thought to be beyond naked eye visibility. Theoretically it might be possible for a very keen eyed observer to see it in exceptional conditions but I can't find a mention of anyone who has - discussion here: Why has no one seen Neptune with the naked eye?

So theoretically a very patient, careful and thorough ancient astronomer with excellent seeing conditions could have done maps of the entire sky, plotting every star right down to the faintest visible, and then theoretically they could have discovered, Uranus, also Vesta, and potentially Ceres and just possibly, if they found a very keen eyed observer to do the observations, Neptune (though that's a bit of a stretch).

But though they did do star charts, they didn't manage to do it to quite this level of thoroughness and they never discovered them. Tycho Brahe, who made it his life's work to observe the stars with naked eye observations in the 1500s didn't discover Uranus.

It is difficult to plot the positions of the stars in the sky. You  could use things like this to do it accurately without a telescope:

(Jantar Mantar, Delhi)

Jantar Mantar - Ancient Astronomical Observatories of India

Jantar Mantar, New Delhi

This observatory was actually built after the invention of the telescope but it was used for naked eye observation. The ancient astronomers could in principle have built something like this and used it to do extremely accurate star maps, but never did (as far as we know anyway).

In ancient times the instrument of choice for star mapping was the Astrolabe  which was later developed into the spherical astrolabe or Armillary sphere (Nicolaus Copernicus - Amilliary sphere Observing with the Amilliary sphere,) (see also Hipparchus Astronomical instruments and astrometry) 

Tycho Brahe used an especially large four foot diameter Armilliary Sphere for his naked eye observations. With this instrument he made the observations that Kepler then later used to prove that the planets followed elliptical rather than circular orbits.

Full scale replica of the armilliary sphere used by Tycho Brahe for his observations in the late 1500s

Pluto is well beyond naked eye visibility.