Re the work.
This is the age I teach as I work in infants.
We have to set the full curriculum but my personal thoughts are, for this age group, to focus in key stuff and then follow your child's interests.
So daily, of at all possible:
5-10 minutes - phonics practise.
Daily reading - them reading to you and a bedtime story from you to them (or an audio book, CBeebies story time if struggling)
Every day maths - you could look at the concepts being taught that week and just incorporate them into daily activities.
Daily writing for 5-10 min.
For example:
Last week in EYFS we looked at the number 9, a circle and the concept was capacity. So every day tasks could be the number 9 number blocks programme, the numberblocks app/game online, capacity by using jugs and beakers in the bath, circles hunt in house.
Year 1 was directions and position. So daily games could be pretending to be a robot and telling each other to turn, move forward/backward, etc; a computer game such as jit5 turtle or Kodak etc/Beebot, drawing a maze.
In English last week reception were reading the gingerbread man. Activities at home could be to retell the story, make a puppet from craft, bake a gingerbread man (lots of maths in that too), listen to story online, use a phone/text/voice message to 'interview' the fox, etc.
Year 1 were looking at non fiction books and key features. Chose a topic of interest and write 1-2 sentences a day with a picture. May not be the school,work but it's writing, using capital let's and full stops, etc.
Then let them pick and choose from the non core subjects if something takes their fancy or let them do their own stuff. Most children's home activities at age 5 are learning opportunities. Board games, Lego, role play, playing with dolls, cars, etc.