Nope...
From your config:
Either mail.washington.com or 2mail.washington.com will be tried first. Both have the same metric so it is not possible to say which will be tried first.
If this fails, then the next MX will be tried (whichever of the above that hasn't been tried)
If that fails, then backup.isp.com
If that fails, we start at the top again after waiting the configured retry interval
Ideally, your MX records should be configured as follows:
mail.washington.com Preference=5
2mail.washington.com Preference=10
backup.isp.com Preference = 99
In other words, remove the ambiguity on which MX gets tried first.