Based upon audit report invest your money where you lag. Backlinks and On Page SEO settings are thing where most people lack.
Backlinks are highly important to rank. So try to hire quality writers and try to post some guest post on various blogs related to your niche.
Invest few amount of money and time in improving on page SEO parameters of your site.
The truth is that the real answer is going to be heavily dependent on where you currently are, what your resources are and what your competition is like.
Reach out to me at mark [at] afterwire.com.au and I would be happy to point you in the right direction. Not that I am trying to sell you in anyway but I have a special passion about people not getting screwed over with questionable advice in an industry filled with "self described experts".
So if I had $5k now to spend:
0. Do an audit or have someone do an audit to see that you're not screwing something up completely. 1. AdWords, if you know that you convert well enough to turn a profit. 2. Internal content stuff: a blog, whitepapers, whatever. 3. External content stuff: 20 backlinks on >PR3 sites should move the needle for sure.
$5k may also do nearly nothing at all depending on what you're trying to rank for. Even medium-sized eCommerce folks probably spend $20k a month on getting backlinks from external sites.
You or an employee should become super familiar with Google Analytics (or another package) and Google Webmaster Tools. You need to measure traffic and make sure your site is being crawled. This is also the best info you will get on rankings.
I hesitate to tell you where to spend $5k. Investing in people would be best. The best solution I could give is to buy the traffic through AdWords.
Do not buy links.
Content is important. Make sure your Title tags are good. But content is close to your core business so I wouldn't necessarily throw $5K at it.
Not sure how you would buy press.
Xenu link sleuth is a great tool.
o Never remove old pages, just update them. This prevents braking incoming backlinks.
o Take a look at letsencrypt.org. (Avoid halfway-HTTPS like CloudFlare etc)
o (etc)
Cover all the basics and keep the money.