Pages v5.5.3 is an entirely different application than Pages '09 v4.3, and there is no Document Inspector. In the View menu, you can select Show Word Count. This will pop a floating panel at document center bottom. When you pass your pointer over it, arrows will appear. Click on the arrows, and a pop-up shows you some statistics. The one you select will be what is displayed in the floating panel. This is Apple's answer to the Info tab in your Document Inspector image.
The Author field is in the Pages Preferences Rulers panel. It will only be used for changes and comments. The Document panel can be reached by clicking the Document icon on the Toolbar. When you use the Insert menu, and select Table of Contents ▸ Document, the TOC will be built, and a Table of Contents Paragraph Styles will appear on the right. This replaces the TOC tab in your image above from Pages '09 Document Inspector.
You should strongly consider obtaining the free WordService collection of services from the OS X App Store. There is a Statistics service that reports information on the selected text, and Sort Ascending/Descending services which are handy, since Pages v5 doesn't address these either. The download installs these services, but does not enable them. You can do this in System Preferences ▸ Keyboard ▸ Shortcuts ▸ Services. Scroll down for WordService:Statistics…, etc. The WordService application will be in your Launchpad items. Run it and click its Help button. This will open Preview with a explanatory PDF about WordService items and what they do.