jmc

To express 87 in base 2, first note that $2^6=64$ is the largest power of 2 which is less than 87. Therefore, the first non-zero digit goes in the 7th place to the left of the decimal point. Since $2^4=16$ is the highest power of 2 less than $87-64=23$, the next non-zero digit goes in the 5th place to the left of the decimal point. Continuing this process, we find $87=2^6+2^4+2^2+2^1+2^0$, so $87_{10}=1010111_2$. Similarly, we find $87=3^4+2\cdot 3^1$ so $87_{10}=10020_3$. The difference between 7 digits and 5 digits is $\boxed{2}$ digits.