根据下列句子及所给汉语注释，写出空缺处各单词的正确形式，每空只写一词。

1. No one helped Jack. He worked out the math problem by ________ (他).

2. ________ (浪费) time means killing yourself.

3. I didn't _________ (认识到) that I was wrong until he told me.

4. We can _________ (容易) become unhappy unless we deal with our problems.

5. We'll have a football match on _______ (星期五) afternoon.