What is the 2x5 swap rate? here 2x5 swap rate refers to the 3-year swap, 2 years forward.
Give or take, should be 6.50%. I got this result by applying (5 * 5y swap - 2 * 2y swap) / (5 - 2). Clearly this is not exact and I feel a bit ashamed to publish it on a quant forum.
Assuming these are par rates for annual swaps, if you bootstrap the curve with DF = (1 - par * sum of dfs from prev annual payments) / (1 + par), you get:
1y 0.952381 2y 0.902613 3y 0.851161 4y 0.798483 5y 0.745020
The 2y3y swap rate would be (df2y - df5y) / sum(df3y, df4y, df5y), i.e., 6.581%