The Trustworthy achievement requires the player to get 5 allies up to the maximum trust value of 100.
Ming Released State Strategy
One possible strategy to get the achievement with relative ease, is to play as Ming, use return province to make 5 one province nations that are entirely surrounded by Ming, such as Miao, Yi, Wu, Shun and Qi, ally those nations, and then play out the game. Make sure to select provinces to return which do not border each other, as this will allow the released states to rival each other, which can make keeping an alliance with them difficult. Such a strategy requires Ming to be over the diplomatic relations limit and so selecting an idea group which increases the number of relations allowed, such as Expansion, Diplomatic and Influence should be considered.
Using Influence nation Great Power Action increases trust by 5 per usage effectively giving 5 trust each 10 years, significantly reducing the time needed to accumulate 100 trust. Monetary cost is insignificant as the nations being influenced are small.
Ming Base Game Strategy
If you have only the base game you can't release independent one province nations as above, you can only release vassals. Then you will have to wait 5 years for the truce to burn off, AND have 10 prestige to lose when you revoke their vassalization. While this is possible, it can be painful and time consuming.
A better method is the following: First, start claim fabrication on Lan Xang and Mong Yang. Then take the mission to annex Dai Viet. Once the claims are complete, attack. When you defeat Dai Viet, release either Tonkin or Annam and annex the rest. Then send the new nation a royal marriage, an alliance, and guarantee them.
If you previously released Annam, when you defeat Lan Xang you can release either Luang Prabang or Muan Phuang. If you previously released Tonkin, release Luang Prabang. Then send the new nation a royal marriage, an alliance, and guarantee them.
The next step is to annex Mong Yang entirely. Its gold mine is nice, and its territory is the perfect springboard for the last allies you want: Sadiya, Taungu, and Manipur. If these nations still exist, then send them a royal marriage, an alliance, and guarantee them. If they don't, fabricate on the nation that has conquered them, release them in the peace deal, and send them a royal marriage, an alliance, and a guarantee.
Finally, entirely annex or push back any nations that border your little allies. First, this keeps your allies from declaring offensive wars into nations and alliance webs you may not want to fight. Second, this protects your allies from serious harm if another ally of theirs calls them into a war that they lose. Your ally can only lose their treasury and manpower, not territory. This protects all the time you've invested in building their trust towards you.
At this point, you can hit speed 5 and wait for 100-200 years to go by, or keep playing as normal.