In setting A-cart up,
1. Did you create a database with username and password?
2. If yes, was that supplied correctly during the setup process?
3. If the above are true, then A-cart should install correctly.
For the PHP version, if you have C-panel and a server that correctly addresses things, there should be a link there for PHP Version Check that and possibly you can up the PHP version to 5.6.
Now, if you still get errors, look at the error and again go to PHP Version. There you should be able to choose what modules are active.
Take a look at everything and if you can give more detail, the solutioin should be fairly easy.
And last but most important, how did you upload the files? Make sure your FTP client is set to binary and not auto. Many errors occur if Auto is selected. My suggestion is Filezilla. Been around forever and is constantly supported. You can set binary transfer easily.