Using the provided dataset, construct a frequency distribution table, identify the modal score, and calculate the probability of a student scoring more than 5 marks.

From the frequency table, the highest frequency is 6, which corresponds to the score of 6.
The modal score is $\boxed{\textbf{6}}$.

Number of students who scored more than 5 marks = (Frequency of 6) + (Frequency of 7) + (Frequency of 8) + (Frequency of 9) + (Frequency of 10)
Number of students who scored more than 5 marks = $6 + 4 + 2 + 3 + 1 = 16$
Total number of students = 29
Probability = $\frac{\text{Number of students scoring > 5}}{\text{Total number of students}} = \frac{16}{29}$
The probability is $\boxed{\frac{\textbf{16}}{\textbf{29}}}$.

c) To calculate the arithmetic mean using an assumed mean of 6, we use the formula $\bar{x} = A + \frac{\sum fd}{\sum f}$, where $A$ is the assumed mean, $f$ is the frequency, and $d = x - A$ is the deviation.

Assumed mean ($A$) = 6.

$\sum fd = -18$
$\sum f = 29$
$\bar{x} = A + \frac{\sum fd}{\sum f}$
$\bar{x} = 6 + \frac{-18}{29}$
$\bar{x} = 6 - \frac{18}{29}$
$\bar{x} = 6 - 0.620689...$
$\bar{x} \approx 5.379$
The arithmetic mean score is approximately $\boxed{\textbf{5.38}}$.