Blessed : 4, 5 and 6 count on succeeding on tests

Does being blessed effect the roll of 5 and 6 to remove a condition upon resting even though does not say the word test on that specific roll?

Nope. Instructions referring to specific results are unaffected by Blessings / Curses. You can check this on the Reference Guide, pag. 12:

Q. Is every roll considered a test?
A. No. An effect that tells you to roll a specific number of dice (such as the reckoning effect on a Cursed Condition) is not a test. These rolls cannot be rerolled or modified by effects that affect tests.