We use the ETC books for that age. My 5yo is still working through the ETC primers. I like that it doubles as phonics and handwriting! If that’s too much, many children like to “write” letters in a tray of rice, sand, applesauce, pudding, etc. They get the letter strokes down without having to hold a pencil (and they usually find it fun). 😉
For first grade, I add a bit of copywork and keep it around 5-10 minutes of writing. They start with a poem line per day and work up to a stanza a day (or more) as they are able. If they are doing a notebook page or other writing, I’ll often have my 1st/2nd grader skip the copywork. I’ve noticed my DS doesn’t write as well as DD which seems fairly common for young boys. I keep an eye on DS and try to make sure he’s not getting too frustrated with writing…some days he’s capable of more writing than other days.
ETA: My DC also enjoy making their own books. They love to draw and will go back and add words to their pictures. It’s a fun way to get them writing (and they don’t consider it “school”).