【Answer】 7 sheets.
【Analysis】Key point: Equivalent substitution 2 Gold $=5$ Red; 1 Gold $=1$ Red +1 Silver, then 2 Gold $=2$ Red +2 Silver; so 2 Silver $=3$ Red. Party A has 3 Gold, 3 Gold $=3$ Red +3 Silver; originally also has 3 Red, in total 6 Red $=4$ Silver. Therefore, Party A can exchange for a total of $3+4=7$ (sheets) of silver card paper.
15. 5 red card papers can be exchanged for 2 gold card papers, 1 gold card paper can be exchanged for 1 red card paper and 1 silver card paper. Person A has 3 red card papers and 3 gold card papers, and can get ( ) silver card papers.