Creating a Trigger to Update Matching Records in Another Table
Here is an example of joining the virtual inserted table with TABLEB.

--demo setup
Drop table if exists TableA
Drop table if exists TableB

Create table TableA (Field1 varchar(20), Field2 varchar(20), Field5 varchar(20))
Create table TableB (Field1 varchar(20), Field2 varchar(20), Field3 varchar(20))

insert into TableB(Field1,Field2,Field3) values('one','two','three')
insert into TableB(Field1,Field2,Field3) values('four','five','six')
go
--the trigger
CREATE TRIGGER I_Am_A_Trigger ON TableA
AFTER INSERT
AS
UPDATE tb
SET tb.[Field3] = 'Hello World'
FROM inserted i
JOIN TableB tb
    ON i.Field5 = 'ABC'     --make sure to only join where the inserted Field5 was 'ABC'
        AND tb.[Field1] = i.[Field1]
        AND tb.[Field2] = i.[Field2]
GO

insert into TableA(Field1,Field2,Field5) values
('one','two','abc')

select * from TableB




| Field1 | Field2 | Field3      |
|--------|--------|-------------|
| one    | two    | Hello World |
| four   | five   | six         |


Including a check on Inserted.Field5 in the UPDATE statement takes care of multiple inserts; only those inserted rows where Field5 has the correct value will be used to update tableB.