After 5 pulse dye laser treatments, there have been little/no results. How can I get rid of these red spots and veins? (Photo)

For rosacea, I like a combination approach, using lasers (ProYellow, Pulsed Dye/Vbeam, Excel V) and botox to the cheeks. This makes dramatic changes in color and symptoms. Please see an expert for a formal consultation. Best, Dr. Emer.

You may be undertreated with the pulsed dye technology and laser settings may need to be adjusted for better outcome.As mentioned, efficacy from pulsed dye lasers is related to destruction of blood vessels with expected bruising and unfortunately, potential for hyperpigmentation, hence the need to use such products. Link is provided for more information.
Pulsed dye laser can cause bruising and swelling and I precondition and treat my patients with a bioflavonoid product called Swell-x pt (post treatment) and also an oral supplement for PIH relief called Scler-X and I find them to be effective. 
For hyperpigmentation relief we use a HQ and non HQ based creams in  the U.S. called Melarase.
Best to inform the physician under whose guidance you got these results.
Hratch L Karamanoukian MD FACS

After five treatments of the pulsed dye V-Beam laser your rosacea should be much better.  You may need to combine these treatments with topical creams like Metrogel or Finacea or Klaron. Please consult an expert for the best dermatologic treatment.  Best, Dr. Green