smc

Let $a_1=a,a_2=b$, so $5a+8b=120$. Now $8b$ and $120$ are divisible by $8$, so $5a$ is divisible by 8, so $a$ is divisible by 8. It's now easy to try the multiples of $8$ to get that $a=8,b=10$ (all the other possibilities violate the condition $a<b$, which comes from the fact that the sequence is increasing). Hence $a_8=8a+13b=8\times 8+13\times 10=194$. $\boxed{194}$