7. Arrange the positive integers whose sum of digits is 5 in ascending order to form a sequence. Then 2012 is the $\qquad$th term of this sequence.
7.38.

To represent 5 as the sum of no more than four positive integers, there are six methods, that is
$$
\begin{array}{l}
5=1+4=2+3=1+1+3 \\
=1+2+2=1+1+1+2 .
\end{array}
$$

When filling them into a $1 \times 4$ grid, positions that are not filled are supplemented with 0. Then $\{5\}$ has 3 ways of filling; $\{1,4\}$ has 9 ways of filling; $\{2,3\}$ has 7 ways of filling; $\{1,1,3\}$ has 9 ways of filling; $\{1,2,2\}$ has 7 ways of filling; $\{1,1,1,2\}$ has 3 ways of filling. 
There are a total of 38 ways of filling, with 2012 being the largest.
Therefore, 2012 is the 38th term.