graphics – Plotting a normal curve over a histogram

With your definitions of rolls and sums, you can find the parameters for the corresponding normal distribution by calculating the mean and standard deviation of sums directly, using Mean and StandardDeviation, or more generally using FindDistributionParameters:

pdf = PDF[NormalDistribution[mu, sigma] /. 
   FindDistributionParameters[sums, NormalDistribution[mu, sigma]]]

With those in hand, you can plot the histogram and the PDF of the calculated distribution. Here I shown them both scaled as PDFs:

Show[
 Plot[pdf[x], {x, 0, 35}, PlotStyle -> Directive[Thickness[0.01], Red]],
 Histogram[sums, {0.5, 31.5, 1}, "PDF"]
]

combined histogram and pdf

Alternatively if you want it expressed in counts, you have to account for the total number of rolls:

Show[
 Plot[10000 pdf[x], {x, 0, 35}, PlotStyle -> Directive[Thickness[0.01], Red]],
 Histogram[sums, {0.5, 31.5, 1}]
]

overlay of histogram and PDF scaled for counts


Incidentally, I would recommend calculating rolls in one go as follows, rather than with nested tables:

rolls = RandomChoice[Range[6], {10000, 5}];