(5/7a)-3+3/a<5a. Multiply through by 7a: 5-21a+21<35a^2 assuming a>0.
35a^2+21a-26>0 has irrational roots one of which is negative, which reverses the inequality.
The positive root is 0.61261 approx, and the negative root is -1.21261.
To satisfy the inequality, a<-1.21261 or a>0.61261.
To appreciate this better, 35a^2+21a-26 is a parabola which cuts the a axis (horizontal) at the roots. It's U-shaped so the vertex is below the intersection points. This means the parabola equation is negative between the roots, so it's positive outside the roots. Therefore a<negative root and a>positive root satisfies the inequality.
It's possible the question is supposed to read differently. Parentheses help to make the intention clear. If the first term is 5/(7a-3) the result is a cubic which doesn't factorise and the solution is more complicated involving an irrational root.
Another interpretation: 5/(7a-3+(3/a))<5a; 5a/(7a^2-3a+3)<5a; 1/(7a^2-3a+3)<1; 1<7a^2-3a+3; 7a^2-3a+2>0. This has no real roots and is always positive for all a. So this interpretation is going nowhere!