There's as much risk that your 5x7's will not have correct color as there is for a larger print. The only difference is that the larger print costs more.
You need to take care of things on your end and your printer needs to take care of things on their end. That means you need to have a properly color-balanced display so that the colors you see are accurate and should appear the same on any other display which is ALSO color-balanced (calibrated.)
Printers get calibrated as well but it's more specific... a printer has to be calibrated for both the specific ink AND paper combination being used. If you switch to a different paper you have to recalibrate the printer.
Some labs make their printer profiles available to you for download so that you can load the printer profile and proof the image based on the color gamut of the printer. It also allows the computer to adjust the colors so that they come out right on the printer (e.g. suppose a printer doesn't saturate a certain color as much as it needs to to produce accurate color ... the profile would tell the computer that it needs to artificially boost saturation so that when it's printed the image will appear correct.)
You can check sites like:
Using Printer Profiles with Digital Labs
They explain the profile and they have a link on that page that will let you locate and download the profile of printers at nearby labs. Costco (of all places) actually profiles their printers and the profiles are available for downloads. Just be warned that you must download the profile for the SPECIFIC PRINTER (the profiles are not generic.) I've never used them so I don't know if they support printing 20x30 prints in the store or if the only way you get that is by mail.
Adorama (adormapix.com) says you should either (a) convert your images to the sRGB color space or (b) download their printer profiles and install them (they have different profiles for different printers and papers... so you have to download the correct profile) and this will give you better color matching control.
You should contact the lab before submitting your prints if you have any questions.