It appears that you cannot.
The issue here is not copyright. Titles and short phrases generally aren't protected by copyright — there is trademark law for that. Dungeons & Dragons certainly is a trademark, but even that isn't really the point here — you can probably use trademarks in a nominative sense even without special permission (hello, Boston Marathon). The important thing is: you want to use 5E stuff beyond just the name, and the OGL — the Open Game License — is what lets you do that. If you want use that license, you have to do what it says. The relevant section is:
- Use of Product Identity: You agree not to use any Product Identity, including as an indication as to compatibility, except as expressly licensed in another, independent Agreement with the owner of each element of that Product Identity. You agree not to indicate compatibility or co-adaptability with any Trademark or Registered Trademark in conjunction with a work containing Open Game Content except as expressly licensed in another, independent Agreement with the owner of such Trademark or Registered Trade mark. The use of any Product Identity in Open Game Content does not constitute a challenge to the ownership of that Product Identity. The owner of any Product Identity used in Open Game Content shall retain all rights, title and interest in and to that Product Identity.
... and in the 5E SRD, the phrase "Dungeons & Dragons" is clearly designated as "Product Identity" — in fact, it's the first thing listed. So, unless you have a separate agreement, it looks like the answer is no — but, of course, keep in mind that I am not a lawyer, and this is just the interpretation of some guy on the Internet.
Note that the wording specifically forbids use of this "Product Identity" — including "Dungeons & Dragons" — in conjunction with a work, not just "in the work itself". This would appear to cover the website situation. This is probably more restrictive than normal trademark rules — but that's basically part of the price you pay in order to get the benefits the OGL grants you.
As with "Marathon Monday" or "The Big Game" in the sports world, you'll probably need to find an alternate phrase which your audience will understand to indicate compatibility without violating the license.