"Uploaded unsupported trim size" And how to I make Ink Coverage premium print?

I've never used Lulu, so I'm speculating, but I suspect there are nsome rounding error problems in the system someplace, though I can't see where they got the PDF size in the message based on your document setup.

First off, you should download and use their template and joboptions files: https://www.lulu.com/create/print-books (make sure you choose the A5 size from the dropdown.

Frankly, in my opinion, the template leaves something to be desired, but it is usable. The first thing I did was open it and check the Document setup. It is NOT set up at 5.83 x 8.27 inches, it is set up im millimeters (not surprinsing for a metric format) and the quoted English dimensions are rounded up which may be one source of error. They also use a 1.75 mm (.125 inch) bleed valuse, which is standard, where your dialog shows twice that, and you've added a slug value which they do not use. This is probably also part of the problem with the PDF size.

The downloaded template has a master page with a visual guide to margins and bleeds on a separate locked layer, and this layer must be turned off before you submit the book. I would go further and set the layer to Non-Printing to avoid any possibilty of output (one of my percieved shortcomings in the template) by right-clicking the layer name, choosing Layer Options, and UNchecking the Print Layer box in the dialog that will open. Leave the layer locked so you cannot add objects to it. I would also move it to the bottom of the layer stack.

Included in the downloaded package is a .joboptions file that you can use for export for the Standard Print output. They are expecting US Web Coated (SWOP 2) as the CMYK working space profile, and sRGB for RGB. Unfortunately, the Template does not conform to the CMYK profile and is using Coated GRACol 2006 (the profile they use for their Premium print service) which supports a higher total ink coverage. This is most likely the source of the Ink Coverage warning.

SWOP 2 allows for 300% total ink which is easy to exceed in dark areas. As I recall GRACol allows 330%. Total ink valus are the sum of the densities of each of the inks used, so for CMYK 400% is the maximum possible (and that's Registration color). Too much ink makes puddles on the paper and doesn't dry properly. Even the 300% ink limit may be too much for the interior of your book using the standard option, but that would depend on the paper stock.

To see where the problems are, open the Separations Preview Panel (Window > Output > Separations Preview). Areas with more ink than the limit you set will be shown in red. Hover your mouse over them to read the ink values. I see that the Lulu Almost Black swatch they use for the rich black text on the template is 329% so I'm guessing they will pass that for Premium print, but I would be cautious about it.

If you are going to switch to the Premium service, I think you can use the template as-is and export using the job options they provide, as long as you don't exceed the ink coverage limits in your illustrations. I'm hoping Rob Day will chime in here -- he's a lot better at this stuff than I am at this point, but if there are ink problems I think you can do a couple of things to solve them without editing the illustrations.

First, for standard print quality, go to Edit > Assign Profiles and assign SWOP 2 for CMYK. You don't need to reassign profiles for Premium.

Next, when exporting the PDF, start with the Lulu joboptions, but under Output change the dropdown from No Color Conversion to Convert to Profile. The profile should automatically populate withthe document working space, SWOP 2 if you reassigned, or GRACol if not. This will remap any over-ink colors into in-gamut colors, but it may also shift your in-gamut colors slightly.