This is the 3505th most frequent Polish word.
śląski
"Śląski" means "Silesian," referring to something or someone from or related to Silesia, a historical region in Central Europe.
"Śląskiem" here refers to the region of Silesia in Poland, denoted by its name and functioning as a proper noun in the instrumental case.
Mieszkam w Śląskiem od pięciu lat.
I have been living in Silesia for five years.
"Śląska" is used adjectivally to describe the cuisine, indicating origin or belonging to the region of Silesia.
Śląska kuchnia jest bardzo smaczna.
Silesian cuisine is very tasty.
"Śląską" is an adjective in its feminine accusative form, describing the noun "tradycję" (tradition) as being of Silesian origin.