First let's call this number x, 5 times the number is 5x and if we increase it by 4 it will be 5x+4 . Now, if 5x+4 is at least equal to 19, it means, it can only be equal to 19 and be greater than 19. So if we show this as an inequality :
[tex]5x+4\ge 19[/tex]
The least value this expression can have is 19, so let's take 19 as the value and solve.
[tex]5x+4=19\\ 5x=19-4\\ 5x=15\\ \\ x=\frac { 15 }{ 5 } \\ \\ x=3[/tex]
So the least possible number that satisfies these conditions is 3.