A reaction $A\to B$ is of the order 2.5 with respect to A. The half-life of the reaction will be given 

$-\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{d}t}=k[\mathrm{A}{]}^{2.5}.$

Hence,$-\frac{\mathrm{d}\left[\mathrm{A}\right]}{[\mathrm{A}{]}^{2.5}}=k\mathrm{d}t.$

Thus

$\frac{1}{[\mathrm{A}{]}^{1.5}}-\frac{1}{[\mathrm{A}{]}_0^{1.5}}=\left(1.5\right)kt$ 

For  $t_{0.5},\left[\mathrm{A}\right]=[\mathrm{A}{]}_0/2$  

Hence 

 $\frac{1}{{\left([\mathrm{A}{]}_0/2\right)}^{1.5}}-\frac{1}{[\mathrm{A}{]}_0^{1.5}}=1.5k{t}_{0.5}\Rightarrow t_{0.5}=\frac{1}{1.5k[\mathrm{A}{]}_0^{1.5}}\left(2^{1.5}-1\right)$