This symbol means that you have to evaluate the generic term [tex]-4n+1[/tex] at n=1,2,3,4,5, and then sum all the terms. Here's the table:
[tex]\begin{array}{c|c}n&-4n+1\\1&-3\\2&-7\\3&-11\\4&-15\\5&-19\end{array}[/tex]
So, their sum is
[tex]-3-7-11-15-19=-55[/tex]
Alternatively, you manipulate the expression to get
[tex]\displaystyle \sum_{n=1}^5(-4n+1) = \sum_{n=1}^5(-4n) + \sum_{n=1}^5 1 = -4\sum_{n=1}^5 n + \sum_{n=1}^5 1[/tex]
For the first sum you can use the formula
[tex]\displaystyle \sum_{n=1}^k n = \dfrac{k(k+1)}{2} \implies \sum_{n=1}^5 n = \dfrac{5\cdot 6}{2} = 15[/tex]
The second sum is simply 1 summed 5 times with itself: 1+1+1+1+1=5.
So, we have
[tex]-4\cdot 15 + 5 = -60+5 = -55[/tex]
