Back taxes are the least of the problem , if I remember they always charge/fine me 1 baht for every month that I'm late paying taxes, plus 100 baht a year for the actual tax. So for 5 years maybe 500 + 60 baht..., I stand be corrected if not right.
Plus compulsory insurance and safety inspection as mentioned above...
But the green book and maybe number plate is expired after 3 years of not paying tax. So that has to be renewed, this is the more complex process. DLT needs to inspect the bike for identification (different from safety inspection) and renew green book etc., not sure about cost, depends on bike size, nothing astronomical I don't think, under 1000 baht I would say..., needs the owner on green book to go to DLT to sort it out..., some forms and ID copies etc. needed...
I'm sure guys who have done this will respond with more accurate info...