As in most cases, it depends quite specifically on the version you're running, but according the Official Magento CE User Guide for v1.9.1, (p.12) it is a System Requirement that you run
Database MySQL 5.6 (Oracle or Percona)
This guide also confirms the same point: although it may be POSSIBLE to run Magento 1.9.1 on MySQL versions prior to 5.6, it is recommended to use 5.6
Although there has been some discussion about the specific tuning parameters needed, and the differences you may encounter if running MySQL on Amazon Web Services RDS, the general consensus seems to support that 5.6 will AT LEAST double the performance of 5.5, with Oracle claiming it's 230% faster on read workloads (over 3x). I'm not sure I'd give their marketing literature the same weight as data-driven benchmarks, but there should be no doubt - you should be running MySQL 5.6 if it's at all possible.
You do need to take absolute performance statements with a grain of salt because of the myriad of tuning options available and massive variances possible between environments. But the overwhelming consensus seems to support that you should be running 5.6 if possible with your webhost.
I'd also recommend you take the time to really dig into Ben Lessani's incredibly thorough deep dive into a similar question. He notes that one of the first things you need to do is define "performance" specifically:
Do you mean the page load time for a single user, or the overall
capacity/total concurrency? The two are very distinctly different -
and not strictly related. It is entirely possible to have a fast store
with limited capacity; or a slow store with lots of capacity.
So when addressing either type of performance:
- Single user perceived page load time
- Total capacity/concurrency
You have to tackle each independently with their own solutions -
especially since each have their own bottlenecks.
There is no easy way to answer this question, not if you want to truly address the issue of performance / scalability and the inevitable tradeoffs that pursuing those objectives may entail.
Magento 1.9 is compatible with MySQL 5.7. You may have a bit of a bumpy start if you have to manually set the sql_mode parameters but in most cases it goes well.
I would heavily suggest however testing on a development server first so if you have to set the params manually you will know what to do as soon as the live version switches. You can take a dump of your database, install magento on the new DB then import the dump to get the best chance of no issues.
Best Answer
It compatible use Magento-1.9.0.1 with PHP 5.6.5 and MySQL 5.6
source : http://devdocs.magento.com/guides/m1x/system-requirements.html
System Requirements for Magento Enterprise Edition and Community Edition (As per magento's documentation)
Magento requires a LAMP or LNMP stack
Operating System Linux x86-64
Web Server Apache 2.x,Nginx 1.7.x
Database MySQL 5.6 (Oracle or Percona)
PHP
Magento CE 1.9.2 and later, Magento EE 1.14.2 and later:
PHP 5.6.x, PHP 5.4.x, PHP 5.5.x
Earlier Magento versions:
PHP 5.4.x,PHP 5.5.x