In Timaeus, Plato names seven planets:

And God made the sun and moon and five other wanderers, as they are called, seven in all, and to each of them he gave a body moving in an orbit, being one of the seven orbits into which the circle of the other was divided. He put the moon in the orbit which was nearest to the earth, the sun in that next, the morning star and Mercury in the orbits which move opposite to the sun but with equal swiftness--this being the reason why they overtake and are overtaken by one another. All these bodies became living creatures, and learnt their appointed tasks, and began to move, the nearer more swiftly, the remoter more slowly, according to the diagonal movement of the other. And since this was controlled by the movement of the same, the seven planets in their courses appeared to describe spirals...

So, we have, all considered as planets:

• The sun
• The moon
• The morning star [i.e. Venus]
• Mercury
• Three other planets - implicitly, Mars, Jupiter, and Saturn, since they're they're visible with the naked eye and would have been known to Plato's contemporaries.

Uranus and Neptune are the only (of the now 8) planets that were discovered in modern times. The other 5 + the earth were all known by ancient cultures.

Mercury, Venus, Mars, Jupiter, Saturn