How many digits does it has?

Matching up all $2's$ and $5's$ : $2^{2016}\times5^{2016}\times5^4=(2\times5)^{2016}\times 5^4=625\times10^{2016} \therefore 2^{2016}\times 5^{2020}$ has $3+2016=\boxed{2019 \text{digits}}$

To find number of digits simply find $[log_{10}2^{2016}5^{2020}]+1$ , where $[.]$ is greatest integer function. Upon calculating logarithmic part we get $2018$ ,

Now $[log_{10}2^{2016}5^{2020}]+1=2018+1=\boxed{2019}$

$2^{2016}×5^{2020}=(2×5)^{2016}×5^{4}=10^{2016}×625$

Now $10^{2016}$ consists of 2017 digits but when multiplied with 625 it will consist of $\boxed{2019}$ digits.

2^2016 x 5^2020 = 10^2016 x 625 = 2016 + 3 = 2019 digits