If a child is regularly using a dynamic tripod grasp without needing to be reminded to do so, there is nothing to say that beginning to use a cursive (joined) handwriting style could do any harm. In fact, the use of cursive writing has been shown to support children with their spelling, allowing them to write familiar words with automaticity and accuracy. (Children who have dyslexia, and who do not have handwriting difficulties arising from hypermobility, dyspraxia, etc., are encouraged to use joined writing in their work). This may be why your daughter's teachers have set the joined writing of whole words as holiday homework - either to support the class in learning the spellings of specific words to be copied (depending on what the words are) or to set her on the track to begin to use cursive writing with the intention of helping them to learn to 'remember' spelling / letter strings with greater automaticity.
The problem with going about this as a whole class activity/ approach is that it's wholly inappropriate for those children who haven't acquired/ developed the most appropriate handwriting grasp - or who physically won't be able to.
I'd suggest that you have a look at your daughter's handwriting grasp first of all, as this is key.
A dynamic tripod grasp is optimal in order to be able to join letters in a joined, rhythmic and fluid manner: www.google.co.uk/search?q=children+handwriting+grasp&ie=UTF-8&oe=UTF-8&hl=en&client=safari#facrc=_&imgrc=6_Rda4JbK5geXM%253A%3Bundefined%3Bhttp%253A%252F%252Fmissmancy.com%252Fwp-content%252Fuploads%252F2012%252F07%252Fgrasps.jpg%3Bhttp%253A%252F%252Fmissmancy.com%252Fcategory%252Fhandwriting-coloring-skills%252Fgrasp%252Fpage%252F2%252F%3B600%3B307
This is unusual in a child of five years old. There are plenty of wonderful exercises and activities on one of the the sites recommended by Ferguson (teach handwriting.co.uk) that will strengthen and support the fine motor skills and muscles of the hand and wrist:
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www.teachhandwriting.co.uk/handwriting-warm-up-exercises.html
2.
www.teachhandwriting.co.uk/more-activities-help-develop-handwriting-skills.html
Tips to encourage use/ formation of tripod grasp: www.teachhandwriting.co.uk/tips-forming-tripod-grip.html
I'm going on about the importance of the handwriting grasp as its such a difficult area to corrct / adjust once a child has become accustomed to holding a pencil incorrectly.
It is important to note that there are many children who have hypermobility in the finger joints. For these children, using the usually recommended dynamic tripod grasp would cause them to have aching fingers, strain and to find writing for more than a few minutes at a time to be very difficult. These are the children who need to be allowed to adjust their handwriting grasp to suit their comfort. To 'force' these children to use a dynamic tripod grasp is actually rather cruel and highly likely to put them off writing as it'll be very uncomfortable for them after a few minutes. Many handwriting grips can be found for this purpose but these children often 'create' their own handwriting grasp that ought to be accepted if it is comfortable and SUSTAINABLE for them. However, they WOULD really benefit from working hard on the strengthening exercises (1&2) linked above.