Step 1 :The given equation is in the form of an exponential function, $y = ab^x$. When this is plotted on a semilog scale, it becomes a straight line. The slope of this line is the logarithm of the base of the exponential function, and the y-intercept is the logarithm of the coefficient of the exponential function.
Step 2 :In this case, the base of the exponential function is 1.1 and the coefficient is 5. Therefore, the slope of the line, m, is $\log(1.1)$ and the y-intercept, b, is $\log(5)$.
Step 3 :Calculating these values, we find that $m = \log(1.1) \approx 0.0414$ and $b = \log(5) \approx 0.699$.
Step 4 :Therefore, the linearized equation of $y=5(1.1)^{x}$ on a semilog scale graph is $\log (y)=0.0414x+0.699$. So, $m = \boxed{0.0414}$ and $b = \boxed{0.699}$.