Let's start with the inference that the big drops ($4.81 \to 4.68$, $4.73 \to 4.62$) are caused by rankings of $1$. (This might be wrong, but it's a reasonable first guess to get us started.)
Call rating $i$ by the name $x_i$, and call the sum of the first $n$ ratings by the name $s_n := \sum_{i=1}^n x_i$. After $n$ total ratings, you had an average of $4.81$; that is, $\frac{s_n}{n} \approx 4.81$. You then received what may have been a rating of $1$, and it dragged your answer down; this would suggest that perhaps $\frac{s_n + 1}{n+1} \approx 4.68$. We now have two equations with two unknowns that we can solve. By substituting $4.81 n$ for $s_n$ in the second equation, we get
$$\frac{4.81 n + 1}{n + 1} \approx 4.68 \implies n \approx 28.$$
But, this solution doesn't seem quite right; we need a whole number $s_{28}$ such that $s_{28} / 28 \approx 4.81$, and there isn't one. Using $s_{28} = 134$ would give an average of $4.79$, and using $s_{28} = 135$ would give an average of $4.82$. If we try the nearby number $n = 27$, we note that having $s_{27} = 130$ would give the average $130 / 27 \approx 4.81$ we wanted, and if you then received a one-star rating, the average $131/28$ would be $4.68$. This suggests we might be on to something.
Now, let's check whether this is consistent with the rest of the table, and we'll see if we can infer the individual ratings after number 27. To spoil a surprise, I think you missed one rating early on in the tracking. Individual ratings I inferred are in blue, and the rating I think you missed is in red.
$$\begin{array}{r | c| c | l}
n & x_n & s_n & \text{avg} = s_n / n\\ \hline
27 & & 130 & 130 / 27 \approx 4.81 \\
28 & \color{blue}{1} & 131 & 131 / 28 \approx 4.68 \\
\color{red}{29} & \color{blue}{5} & \color{red}{136} & \color{red}{4.69} \\
30 & \color{blue}{5} & 141 & 4.70 \\
31 & \color{blue}{5} & 146 & 4.71 \\
32 & \color{blue}{5} & 151 & 4.72 \\
33 & \color{blue}{5} & 156 & 4.73 \\
34 & \color{blue}{\mathbb 1^*} & 157 & 4.62 \\
35 & \color{blue}{4} & 161 & 4.60 \\
36 & \color{blue}{4} & 165 & 4.58 \\
37 & \color{blue}{5} & 170 & 4.59 \\
38 & \color{blue}{5} & 175 & 4.61
\end{array}$$
So this all fits perfectly, if I'm right that you missed a single rating early on. I think you may have around $\fbox{38}$ ratings so far.
Of course, I'm drawing some inferences. Maybe you missed even more ratings, for instance. But these data tracked well enough that I feel good about this answer.