I can think of two things that might help you.
First, likelihoods are defined only to a proportionality factor and their utility comes from their use in a ratio and while they are proportional to the relevant probability, they are not probabilities. That means that if you are uncomfortable with the values in the range of $10^{-65}$ then you could simply multiply them all by $10^{65}$ without changing the ratios. Of course, there is no need to do as the ratio effectively does it for you. The likelihood ratio for the two distributions is about 25 times in favour of the 5,5 distribution over the 6,6 distribution. That would typically be thought of as being fairly strong (but not overwhelmingly strong) support by the data (and the statistical model) for the 5,5 distribution over the 6,6 distribution.
Second, I usually find a plot of the likelihood as a function of a parameter to be helpful. You have set up the system with two parameters that are effectively 'of interest' and so the relevant likelihood function would be three dimensional and thus awkward. (Those dimensions being the population mean, the standard deviation, and the likelihood values.) It would be easier for you to fix one of those parameters and explore the likelihoods as a function of the other. My justification for looking at the full likelihood function rather than a singular ratio of two selected points in parameter space is that it contains more information and it allows the data to speak with less distortion.