[tex]\huge\boxed{\text{The $5$ needs to be negative.}}[/tex]
Since the first binomial is [tex](x-5)[/tex], the [tex]5[/tex] is negative and must be that way when using the table.
Here's the corrected table:
[tex]\begin{array}{c|c|c|}\multicolumn{1}{c}{}&\multicolumn{1}{c}{3x}&\multicolumn{1}{c}{1}\\\cline{2-3}x&3x^2&x\\\cline{2-3}-5&-15x&-5\\\cline{2-3}\end{array}\\\\\\3x^2+x-15x-5\\3x^2-14x-5[/tex]
