Given:

• First term \( \rm a_1 = 5 \)
• Common difference \( \rm d = 11 - 5 = 6 \)

We can use the formula for the sum of the first \( \rm n \) terms of an arithmetic series:

\( \rm S_n = \frac{n}{2}(2a_1 + (n - 1)d) \)

Substitute the given values:

\( \rm S_{20} = \frac{20}{2}(2 \times 5 + (20 - 1) \times 6) \)

\( \rm S_{20} = 10(10 + 19 \times 6) \)

\( \rm S_{20} = 10(10 + 114) \)

\( \rm S_{20} = 10 \times 124 \)

\( \rm S_{20} = 1240 \)

So, the sum of the series \( \rm 5 + 11 + 17 + \ldots \) up to 20 terms is 1240.