Bosonic $\eta$-deformations of Non-integrable Backgrounds

We consider the non-integrable bosonic backgrounds $W_{2,4}\times T^{1,1}$ and $Ad{S}_5\times T^{1,1}$ and derive their bosonic $\eta$-deformed versions using an $r$-matrix that solves the modified Yang-Baxter equation obtaining new integrable deformed backgrounds.