If you were using unaided observations and were unfamiliar with astronomy (and maybe just pen and paper for recording anything), how long should it take to notice that Mercury, Venus, Mars, Jupiter and Saturn move independently of the "fixed stars"? Would some planets be easier or harder to notice than others? I assume that Jupiter and Saturn would be somewhat difficult because they move so slowly and Mercury might be difficult to make observations of at all, but that is just my naive first impression.
It could take a day to discover a planet, if the stars align (literally), and then probably less than a year to find all five planets.
On the 3rd of April 2020 you happen to look up and you notice that the evening star is right in the middle of the Seven sisters (you know the seven sisters because it does look rather special in the sky and the evening star is so bright, so this combination is quite noticeable.
"Has it always been in the seven sisters?" you think to yourself, surely I'd have noticed... so next night you look again.
To your surprise, it has moved noticeably over one night!
From now on you are actively looking for these special moving stars. Over the summer of 2020 you notice two bright stars in the southern sky, and they are clearly further apart at the end of summer than they were at the start. Looking carefully over the summer reveals that they both moved relative to the constellations.
And then in the winter of 2020 into the spring of 2021 you watch as a bright red star move closer and closer to the "V" of the hyades.
Mercury is always hard to spot, but as soon as you do (perhaps in the mornings of July 2020) you know it moves, because it simply isn't in a place where a star is, it moves so fast that its motion is quite obvious.
With naked eye astronomy, there is no reason why you should not identify 5 planets with a year.