No next posts link on category page?

I’ve made my theme from an HTML template and I’m using a page template to show the posts from the Portfolio category.

The category page is showing 5 posts per page, the same as the blog index, but the problem is there is no navigation link to the next page of posts and I don’t know how to fix this.

If you go to the portfolio category in the blog page here, then the links are there, but they aren’t there on the portfolio page.

The code I’m using for the navigation links is:

[Code moderated as per the Forum Rules. Please use the pastebin]

Can anyone help me? I’m not that good at PHP so I don’t really know how to fix this without changing the whole layout of the category page..