A two-deletion correcting code of length $n$ is defined to be a set of binary words such that a codeword can be uniquely identified from any one of its length- ($n-2$) subsequence. A two-deletion correcting code requires at least $2\log n+O(1)$, while the best known explicit construction uses $4\log n+o(\log n)$ redundant bits. In this work, we study this coding problem in the framework of the sequence reconstruction problem and require the receiver to uniquely reconstruct a codeword from any $N\geqslant 2$ of its length- ($n-2$) subsequences. Specifically, we provide an explicit code construction that uniquely reconstructs a codeword from any five of its length-($n-2$) subsequences, using only $2\log n+o(\log n)$ redundant bits.