Algorithm to calculate rating based on multiple reviews (using both review score and quantity)

What you can do, for instance is take the rate of reviews (w weighted mean), divide it by two (in order to reduce the scoring to a scale of $[0,5]$ and add this value to $5(1-e^{-q})$. So the formula becomes $$\text{score}=5p/10+5(1-e^{-q/Q})$$ where $p$ is the review rating and $q$ is the quantity of ratings and you chose for $Q$ an appropriate number that shows what importance you attach to the notion "quantity". An example: An item has $3$ times a revision score of $6$ and $2$ times a revision score of $7$. Then $p=(3.6+2.7)/5=6.4$ if we take $Q=10$ then $5(1-e^{-5/10})\approx 3.88$ so the total score is $3.2+3.9=7.1$ rounded $7$. On the other hand if somebody has $20$ scorings of $6$ then $p=6$ and $5(1-e^{-20/10})\approx 4.58$ so the final score is $3+4.6$ rounded giving $8$. The choice of $Q$ depends on what you call "few", "moderate", "many". As a rule of thumb consider a value $M$ that you consider "moderate" and take $Q=-M/\ln(1/2)\approx 1.44M$. So if you think $100$ is a moderate value then take $Q=144$. Finally you can also replace the equal weight on quantity an quality by a skewed one so that the final formula becomes:$$\text{score}=Pp+10(1-P)(1-e^{-q/Q}))$$ where $P\in [0,1]$ (in the original formula we had $P=0.5$).