Sarah arranges a total of $120$ stamps across $5$ albums.
There are $3$ more stamps in the $2$nd album than the $1$st album.
There are $4$ more stamps in the $3$rd album than the $2$nd album.
There are $5$ more stamps in the $4$th album than the $3$rd album.
There are $6$ more stamps in the $5$th album than the $4$th album.

How many stamps are in the $4$th album?