Is there a way I can run this game at 60ps with my laptop?

Hey guys, how's it going?

So I today I got a new laptop after my old one died and stopped working. Being addicted to this game as I am I decided to install it as quickly as possible but sadly I've noticed that my frames in this computer aren't as good as my old one. On my old Laptop I could get 60 fps with the graphics at low and my power plan on low performance. On my new laptop I have my power plan at balanced and I set my graphical settings at low. While I can get more than 80 fps at the start of the game I drop to 42-45 as soon as the minions spawn and get to lane. Team fights and such can drop me to 24 fps... It's quite ugly.

Here are the specs for this current laptop AMD Quad-Core A8-6410 ProcessorA MD Radeon R5 graphics with 2.0 Ghz 8Gb RAM

This laptop is more up to date and has better specs than the last one, More RAM a better processor (The old one was amd 6) and stuff. The only thing the old laptop had more of was 2.4 Ghz.

So is there something I can do with this laptop than can bump up my frames to 60? I find it very hard to play with 40 something frames.