If they offer a one-click install of Zen Cart, you will be able to use it with 5.2.13.
If they don't have a one-click install, you will have to upload the files yourself and run zc_install, but you will have to edit the zc_install php code to bypass the version check for 5.2.14, else it won't let you install.
Of course, it's always recommended to use the minimum specified versions because there are reasons for those being the specified minimums. In this case 5.2.14 is preferred over 5.2.13 simply for PCI reasons.
Zen Cart v1.5.1 will technically function with PHP 5.2.10 and newer without coding problems imposed by the PHP version.
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Remember: Any code suggestions you see here are merely suggestions. You assume full responsibility for your use of any such suggestions, including any impact ANY alterations you make to your site may have on your PCI compliance.
Furthermore, any advice you see here about PCI matters is merely an opinion, and should not be relied upon as "official". Official PCI information should be obtained from the PCI Security Council directly or from one of their authorized Assessors.