Combining two Likert responses into one composite variable


I've been reading up on this topic for hours and haven't found a solution to my problem. I ran a survey which had 10 questions, split into 5 "topics", that required an answer from strongly disagree to strongly agree. Therefore, I had 2 questions for each topic. Now, I want to combine the two responses from each topic, to give me 5 variables that I can run an ANOVA on. However, I have read that I cannot take the mean of the two variables as this is not correct (i.e. if someone answers Neutral (3) on one, and Strongly Agree (5) on the other question, I cannot take the variable as 4). I have tested the inner correlation though for each topic and there is significant correlation within each topic.

I looked into factor analysis across all 10 questions, but that loads the variables incorrectly into only 3 components, whereas I am wanting 5. So, can I run a factor analysis on just the two variables for each topic to get a principal component score? Is this more accurate/statistically correct than taking the mean score for each topic?