According to this article on Daily Business the Bank of Scotland will issue two new polymer notes in the near future. The next 5- and 10-pound notes will be printed on polymer by De la Rue. There will be a special occasion in November 2015 when 50 special one-off notes will be auctioned picturing children's drawings with the proceeds going to BBC Children in Need.
At the end of the year the design for the new circulating 5-pound note will be unveiled (which will be similar to the current paper note) while the issue date will be the second half of 2016. The new note will be 125 x 66 mm in size, slightly smaller than the current 135 x 70 mm 5-pound note. It won't be until 2017 when we see the new 10-pound printed on polymer.
The current paper 5- an 10-pound notes will be gradually withdrawn from circulation.