This is not a direct answer to the part of your question about the degree to which weather systems within a short period of time can be "linked", but with respect to the difference between a given year and an average value, there are two points to consider.

1. Something like the average you mention, i.e., "5 wet days per month" is just that, an average. For most climatological parameters, a reported mean will represent at least 10 years of data (usually more). Importantly, the mean only tells you about the central tendency, but nothing of the variability. If we were dealing with normally distributed data, you could think about something like the standard deviation as a crude metric of variability. So for your given area, if the average wet days for your month of interest was 5 and had a standard deviation of 1, that would broadly suggest 14 wet days is a lower probability event, but if the standard deviation was 5, that would similarly broadly suggest that the precipitation in that month is more variable (assuming you had enough a long enough set of data where you standard deviations were meaningful). Now in reality, while some climatological variables tend to be close to normally distributed (e.g., temperature), precipitation tends to not be well explained by normal distributions. Instead, distributions like the weibull, logistic, exponential, or GEV are better suited for describing precipitation. For these, we might be interested in the "shape" parameter (or equivalent) for a fit to the distribution of rainfall assuming one of these distributions which would give us a sense of the variability and thus how probable a significant deviation from the mean is.
2. In a similar theme, mean climatological parameters will typically represent averages across a variety of cyclical changes in climate, things like ENSO. We are currently experiencing La Niña, so hypothetically, if for your location in this month, it's typically more wet during La Niña (and perhaps drier during El Niño, where the mean reflects somewhere between the two), then this may not be "out of the ordinary" at all.