Stupid question perhaps, but do you actually go to Zone 5? There are also Zone 1, Zone 1-2, Zone 1-3 and Zone 1-4 tickets available at a lower price if you don't (as well as Zone 1-6 at a higher price).
There are also tickets not including Zone 1 (such as Zone 2-5 or Zone 3-4) which may be of use to you if your train stops within the Zones before terminating (e.g. at West Hampstead, Tottenham Hale or Wimbledon) and you can make your Underground journey from there without passing through any zones your ticket doesn't cover.
To find these fares on BRFares you need to search for "ZONE U" which will then list all the various options in the drop down menu below. Zones 1-5, 1-6 and 2-6 are written as U1245, U1256 and U2356 respectively.
As already suggested, in addition to comparing the price with Contactless/Oyster, you should also compare the price to an outboundary Travelcard. In some cases these are actually cheaper even though they offer unlimited travel on all modes in Zones 1-6 rather than just one Underground/DLR journey.