using their sorcerer spell slots/known slots.
No. (Unless the GM says so.) "Spells: A dragon knows and casts arcane spells as a sorcerer of the level indicated in its specific description. Its caster level depends on its age, as shown for each type."
Some do (the silver, umbral, and gold for example). The norm seems to be no, with exceptions called out somewhere within the basic info for that type.
why does the silver dragon have cleric spells in its bestiary entry?
Planar dragons cast as oracles instead of sorcerers.
why does the silver dragon have cleric spells in its bestiary entry?
Because the * after caster level for Silver Dragons and Gold Dragons say they can cast cleric spells. Silver Dragons and Gold Dragons being able to cast cleric spell is not an error, they have a specific exception to the rule.
oh I see, thanks
I rather doubt it was an oversight. Silver and Gold dragons are often divine intermediaries.
Gold and Silver dragons casting cleric spells predates pathfinder, if memory serves all metalics, together with red and blue dragons could cast cleric spells in 3e.