what are some learning activities or learning games to do with a 5 year old?

You sound like a good mom who wants to help her son have a good foundation for learning so he will be a successful learner in school. I can’t say often enough how important it is for a parent to be involved in their child’s education, so here’s a big pat on the back to you,mom! Make sure you are reading to him every day, and make sure he has access to plenty of reading and writing materials in your home: books, magazines, paper, pencils, pens, crayons, etc. Let him see you using these materials too so you are modeling good literacy skills for him. Take him outside to run, jump, ride a bike, and play. Go for walks together and talk about what you see. Let him help you set the table and cook and do the laundry. He will be learning a wide array of skills from all these activities.

*Teach him his letters one at a time, starting with the letters in his name. Use an upper case letter for the beginning of his name and lower case for the rest of it. He really will understand the difference. Help him find his first letter everywhere, on cereal boxes, in books, on signs, etc. When he can find it and point it out to you, start on the next letter.
*Let him learn to write his name as you are teaching the letters. He can make them with playdough (added bonus: find a play dough recipe on line and make it together…math skills!). You can put rice, pudding, or flour on a cookie sheet and encourage him to draw in it and write his letters in it with his finger. Really fun: put shaving cream on the table (it’s just soap) and draw and write in it with him. As he learns to write his name, encourage him to write it all the time. ("That’s a great picture you made for the refrigerator! Please write your name on it so everyone will know who the artist is!" Also, let him sign his own name to birthday cards or letters you are sending out.
*Let him figure out how many forks, plates, napkins and cups will be needed for dinner and set the table.
*Help him count how many steps it takes to get wherever…across the room to the tv, down the stairs to the washing machine, out to the back yard, etc.
*Get him a pair of child’s scissors and let him cut pictures out of magazines. This builds fine motor strength and control he will need for writing. He can glue the pictures onto paper to make collages to boost creativity.
*Take him to visit public places like the library, the zoo, the park, the museum to help him build social skills and expand his experiences,’
*Talk with him and listen to what he has to say. Ask questions about his stories and comments to encourage language and thought.
*Use adult vocabulary and encourage him to ask what words mean if he hears a word he doesn’t know.

There is no limit to what he can learn in the next year. Don’t push him. Keep it fun and keep building on what you’ve already done so he is always moving forward. And most of all, have fun and treasure these early years, because he will grow up much faster than you want him to!