Adding a Fixed Value to Each Element in a Set (How to Denote)

Question

To denote a set such as, for example, the set of every natural number that is 3 greater than a multiple of 5, would $5\mathbb{N}+3$ be generally understood as $\{8,13,18,23,28,33,\dots\}$? If not, how should I write it instead? I spent quite a bit of time searching the internet for an answer to this, but could not find one. Any help would be appreciated.