From (1) solve for x:
[tex]\begin{gathered} 5x\le1+19 \\ 5x\le20 \\ x\le\frac{20}{5} \\ x\le4 \end{gathered}[/tex]From (2) solve for x:
[tex]\begin{gathered} -4x+3<-6 \\ -4x<-6-3 \\ -4x<-9 \\ x>\frac{-9}{-4} \\ x>\frac{9}{4} \end{gathered}[/tex]the solution is:
[tex]\frac{9}{4}