How do I search movies by price?

You should have this option in your iTunes Store (by clicking on the small arrow directly, which appears when you hover over "Films"):

or if you miss that, how about once you are in the Films section, here;

although, obviously - in dollars!

Perhaps that offer has finished. Alternatively, maybe the offer shown in your screenshot (HD movies $9.99) has replaced it. Have you asked your local friends, who will be looking in the same Store as you?

If there is still no option for low price films, then I guess you only other option is to contact the iTunes Store support, which you should be able to do via Your Account, because as you can see, here in the UK, we do have that option. This does not mean that you should or will have the option in your country.

My screenshot show UK pounds - £5, which is not the same thing as $5 you now mention. In your first post, you mention under $10 - dollars!

In the screenshot you provide, I can clearly see the icon stating HD films at $9.99 - for a limited time. Maybe that's browsing by price, while you wanted search by price. (You see, I am paying attention.) Perhaps, the $10 deal for normal films was also limited time, and also involved browsing, not searching.

Perhaps you should ask the person who told you about this offer.

CrisAnn wrote:

... I was told there was an option to search by price...

In other words, challenge them to prove it or be quiet. After all, one can say anything, even if it isn't actually true. Where did that person get that information from? Has he/she seen it for him/herself, or did the information come from "an unknown source"?