Generically: exponentials beat positive powers; larger (positive) powers beat smaller (positive) powers; (positive) powers beat logarithms.
Among exponentials, you can always convert them all to the same base and compare exponents; larger exponents beat smaller ones. Same for logarithms.
So you know that $10^n$ will grow the fastest; with $2^{\log n}$ you have to be careful, because it looks exponential, but an exponential raised to a logarithm is actually not exponential: $2^{\log n} = e^{(\log n)(\log 2)} = (e^{\log n})^{\log 2} = n^{\log 2},$ so this is actually just a power.
Among the powers, you have $n^{1/2}$, $n^{\log 2}$, $n^{1.5}$, and $n^{5/3}$. Comparing the exponents, we have $\frac{1}{2}\lt \log 2 \lt 1.5 \lt \frac{5}{3}$ so that's the order of growth of the functions. So we have (with $\succ$ meaning "grows faster than") $10^n \succ n^{5/3} \succ n^{1/5} \succ 2^{\log n}=n^{\log 2} \succ \sqrt{n}.$