I think the rule would result in examples like these...
...where the rules says to avoid movement like the first two examples.
The third is OK - by the rule - because there is at least one dissonance.
I haven't seen a rule with the specific wording, but the general principle is...
- use a variety of intervals and motion types to create interesting counterpoint
- use dissonance as a dynamic force to move the music forward.
...do not understand how a concordant movement can be longer than fifth. The only allowed intervals that are larger than 5th are minor 6th and octave.
I think the misunderstanding comes from the rule being poorly worded. Maybe they should use range. "...stepwise movement ranging more than a fifth..." Such movement would be the parts I circled in red. I don't think they mean the size of a melodic leap.
The "concordant" part could refer to melodic intervals like the tritone
F leaping up to
B which is often avoided. That that melodic concord meaning doesn't make sense to specify when the movement is already described as step-wise. I can only assume the concords are those formed in counterpoint with another line.
I'm still not sure where you got this rule. If you don't have a copy of Fux's species counterpoint, you should try to get one. It's one of the seminal counterpoint books. Personally, I have more faith in "rules" when they come from the most authoritative sources... or from real scores.