Any food establishment is entitled to apply for a re-assessment of their food hygiene rating, so that's clearly what the restaurant referred to in your post needs to do. Any newly-opened business has to register with the local authority and should be inspected by that authority within a fairly short space of time.
However I can't see how you (or any customer) could assess a restaurant as having a '5' rating. Much of the assessment process looks at procedures and record-keeping (such as ensuring that there frequent checks on the temperatures of fridges, freezers and food being kept warm, with all of those temperatures being recorded). No customer would normally have access to such information nor, unless they were allowed to make a detailed inspection of the kitchen, to ensure that there are separate, colour-coded knives and chopping boards for fresh meat, cooked meats, fish, etc.