he most important thing you need to remember here is that you're going from an app aimed at the professional or serious hobbyist shooter, to an app that is aimed squarely at the family snapper, probably shooting with an iPhone. Photos is a much less capable app, and much less flexible. Its attraction is the ability to share images across multiple Apple devices, and that's not something a LR 5 user is looking for :) So you might ask if it's the app for you. The fact is that, in import, Photos copies all the images into an opaque set of folders, renames them and they become accessible via Photos only can be off-putting for some users*. I would strongly urge you to move part of your library over - say, one year's worth - and experiment and explore, see it it does what you want and need. This process is non-destructive so it's risk free.
The steps are simple: Export from LR5 to folders in the Finder, then use the Import command in Photos to add them to that library. What you export from LR 5 - in terms of metadata and location, should be picked up by Photos. So, the important step is your exporting.
You'll need to make a choice here also: what do you want in Photos? Your Raws? Your edited versions? Or both? There is no way to maintain the relationship between the Raws and Versions when you move from app to app like this.
*Strictly speaking this is not true. You can run Photos in what is called referenced mode where the files are stored in your own folders. But, and it's a huge but, this is very poorly implemented and is very much an excellent opportunity to create problems in the future. Don't touch it with a barge pole.
Alternatives? Graphic Converter is an excellent app with a pretty good organiser, and the oddly named NeoFinder, which started out as a way to catalogue optical media, now runs as a pretty good photo manager and is also worth a look.