You could use a combination of Variations and Variants to handle that, even if you don't need to track weight or inventory stock for every combination -- see further details on this help page, including the section at the bottom explaining how to combine Variants and Variations:
http://www.e-junkie.com/ej/help.variants.htm
Since the size won't affect the price, for simplicity you'd probably want to use "Variations that tell more..." to offer a menu of ring sizes, and use "Variants having individual price/weight/stock/SKU" only for the silver/gold combinations. You can leave the weight and stock positions empty on each line since you won't be using those. Presuming buyers could order a combination of less than 5 rings, but cannot order any combination of greater than 5 rings, your Variants configuration could look like this:
Option 1 Name: Silver $35 each
Option 2 Name: Gold $110 each
1S-0G,35.00,,,1 Silver Ring,No Gold Ring
2S-0G,70.00,,,2 Silver Rings,No Gold Ring
3S-0G,105.00,,,3 Silver Rings,No Gold Ring
4S-0G,140.00,,,4 Silver Rings,No Gold Ring
5S-0G,175.00,,,5 Silver Rings,No Gold Ring
0S-1G,110.00,,,No Silver Ring,1 Gold Ring
1S-1G,145.00,,,1 Silver Ring,1 Gold Ring
2S-1G,180.00,,,2 Silver Rings,1 Gold Ring
3S-1G,215.00,,,3 Silver Rings,1 Gold Ring
4S-1G,250.00,,,4 Silver Rings,1 Gold Ring
0S-2G,220.00,,,No Silver Ring,2 Gold Rings
1S-2G,255.00,,,1 Silver Ring,2 Gold Rings
2S-2G,290.00,,,2 Silver Rings,2 Gold Rings
3S-2G,325.00,,,3 Silver Rings,2 Gold Rings
0S-3G,330.00,,,No Silver Ring,3 Gold Rings
1S-3G,365.00,,,1 Silver Ring,3 Gold Rings
2S-3G,400.00,,,2 Silver Rings,3 Gold Rings
0S-4G,440.00,,,No Silver Ring,4 Gold Rings
1S-4G,475.00,,,1 Silver Ring,4 Gold Rings
0S-5G,550.00,,,No Silver Ring,5 Gold Rings
