If $f:R^{+}\to B$such that $f\left(x\right)=x^2+4x+5$ is a bijection then the set $B$ is 

The given function is $f\left(x\right)=x^2+4x+5$

Since the funciton is bijective, its codomain and range are same

Hence, the set $B$ is range of the funciton $f\left(x\right)=x^2+4x+5$

It is a quadratic expression, minimum value of the function is $\frac{4ac-b^2}{4a}=\frac{20-16}{4}=1$

Therefore, the range of the function $f\left(x\right)=x^2+4x+5$ is $\boxed{\left[1,\infty \right)}$