I have crawled my website with Screaming Frog, it has roughly 200 pages, most of which are in
example.com/category/product, however, the tool shows me that these are actually on 4-5 clicks away from the homepage. Any ideas as to why this might be?
To find the answer, right-click one of the URLs in question and select Export > Crawl Path Report
You will then get an excel file that will show you the different URLs it crawled through from the starting URL until it discovered the URL in question.
An example of an URL that might be 5 clicks from a home page could be something like:
example.com/ > links too >
example.com/category/ > links too >
example.com/category/sub-category-1/ > links too >
example.com/category/sub-category-2/ > links too >
example.com/category/sub-category-3/ > links too >
As it was mentioned in the first answer, look at crawl path. The cause of what you are seeing, is, that on the site there could be different crawl pathes to the same target.
You, and the crawler, can reach a certain page through different ways: canonical, navigational menu, a content link, a footer link, a link block "most read" and the like...