What is the law regarding dogs and public footpaths?

Usually.

In the UK dogs are considered property and therefore if you attack the dog and harm it you will be held responsible, it's the same as criminal damage. You have recourse under the dangerous dogs act but you must report it to the police and they will take the necessary action against the owner. It might well be satisfying to you to break the dog's neck but don't forget that a fully trained sheepdog can be worth thousands of pounds. Make no mistake, the farmer would sue you after you've been charged with criminal damage and probably animal cruelty as well, it could prove expensive. No, report it and leave it to the correct authorities. I would seriously take on the advice of Crow above.

It all comes down to that vague term under control. This doesn't mean they must be on a lead. It's possible to have well trained dogs under control without a lead though I would think that having 5 dogs controllable without a lead is pushing it. Unless there are signs stating dogs must be on a lead then there's no requirement to have them on leads as long as they are under control. There could be some bylaws stating dogs must be on a lead. you'll have to check.

Depends on where you live...in the UK as long as all the dogs are under control you don't have to have them on a lead......under control means they shouldn't interfer with other people such as jumping up, barking at you ( on lead or not they can be reported if it causes you fear) attacking etc and should immediatly come when called by the owner.........unless it states 'dogs on leads' on a sign prior to entering the right of way they don't have to be on a lead

From what I can see (from looking online, since I don't live in the UK) unless it's posted that the dogs must be on a leash in that area, it's not illegal for her to walk them without one. However, all dogs should be under her control, as in not running into or impeding traffic, and not harassing pedestrians or their pets.

With the exception of rural areas, where they typically don't have any laws about dogs, nearly any and all villages, towns, and cities have leash laws. Not dogs being under control, leash laws.

My dogs are all trained at the highest levels of competitive obedience. I still MUST have them on leash.

That typically goes for any and all forest preserves, etc.

Being able to have one dog, unleashed, on a walk is hard enough. To have five dogs loose is simply irresponsible. You NEVER know what might startle a dog and then have them run into traffic.

Not sure what you mean by "right of way"... but presume if there is no traffic then there is no lead law unless stated.

However, if her dogs interfere with you in any way whatsoever, such as approach and jump at you, then you can report. Obviously also if her dogs foul and she doesn't pick up.

Pepper spray, mace or even RAID will keep the marauders away.

you should be in control at all times, the law is vague on what control is