If this has recently become a problem then try to find out if anything has been changed recently. I know that sounds obvious but as Visvanath says this kind of configuration should handle the load you've described and if it wasn't a problem before and now it is, then it points to something changing.
Changes that often affect the time it takes to load course pages are blocks. Have any blocks been added to course pages or have these blocks been changed recently. You could try creating a new course with no blocks and seeing if that's still performing badly. Alternatively try hiding blocks that are in use (Site administrator → Plugins → Blocks → Manage blocks) and measuring page load time.
PHP 5.5 on Microsoft Windows does have the restrictions you describe. Moving to PHP 7.0 would give you full 64-bit support on Winodws but I'd recommend a test migration to that before making this change on your live site.