There is no need to use two plots commands, just use the pointinterval
option:
plot 'data' pointinterval 5 with linespoints
That plots every line segment, but only every fifth point symbol.
The big advantage is, that you can control the behaviour with set style line
:
set style line 1 lc rgb 'blue' lt 1 lw 2 pt 7 ps 0.75 pi 5
plot 'data' w lp ls 1