I'm Zone 3/4 here -- for years I've felt guilty that I never get my garden in until early June (once, mid-June 
). But, I checked yesterday and our average last frost is June 6th. My mom, who is firmly Zone 3, acts like I'm in the tropics --- but our last/first frost dates actually differ by a little less than a week in each direction.
My gardening projects thus far have been:
1. Started all my old (as in, 8 years old?) sweet pea seeds indoors in hopes of having some to transplant. Despite nicking and soaking overnight in lukewarm water, I had only one germinate (!) .... I haven't decided which plants I'll start in my seedling trays instead now, I might actually do corn. I read in Mother Earth News that corn actually transplants really well. I've never actually started seeds indoors myself, because most springs we are gone for a significant amount of time and wouldn't be able to care for the seedlings while we're gone. Instead, we usually buy seedlings at the local nursery. I err towards the heirlooms, they may not have been started organically but at least they'll be organic once they hit my garden!
2. We tilled the garden last fall, so I was able to plant much earlier than usual this spring. Yesterday, I got my first planting of peas/snow peas planted, as well as onions and my gladiolas. I will wait on everything else 'til the end of the month (or more likely, June).
3. I bought two of those polypropelene potato tubs to try this year. My garden potatoes last year developed scab and from what I've read, that's pretty much THERE in my soil now. So, we'll see whether compost in tubs works better. I haven't decided where I'll put the tubs - I'm toying with the idea of putting them on the front steps, and planting something decorative in the bag with them, as if they're a floral planter. Dh will complain if they are on the lawn itself anywhere, and they need to be accessible for watering.
4. DD1 is in a gardening class at the local nursery. They gave her a tree to plant for Arbor Day. I have no idea where I'll plant it - it's a little Nanking Bush Cherry. Hadn't been on my radar as a plant to squeeze into our garden plan.....
5. My compost heap has been an open one for years, I couldn't decide what I wanted to do for a composter. I've decided that the easiest thing to do will be to make my own vermicompost bin (science project with dd1!) - that way I don't have to trek out to a compost bin during the winter, through ice and snow. We'll see how the project goes, right now I'm feeling really confident - and looking forward to those rich worm castings on my garden!
6. Today, I did the preliminary clearing of my flowerbeds (all the old dead stalks and leaves) - later this spring, I need to re-dig two large beds which have been overtaken by weeds. And I need to go through all the beds and clear the grass etc. yet (I'm only halfway there at this point with the flowerbeds!).
We are CSA members, Heatherdeg, so we actually grow three kinds of things in our garden - flowers, for the girls to enjoy and pick; food to preserve; and foods that our CSA doesn't provide in the quantities we would eat. So, they give us tons of greens --- we don't grow spinach/kale/lettuce/chard anymore. They give a ton of tomatoes; so now I only grow a few tomato plants (a couple Black Krim, and a yellow pear). But we only get a few bunches of peas and green beans, no dry beans, and not a lot of corn. So my garden this year is: peas, beans, dry beans, corn, carrots, parsnips, winter squash (Lakota and Sunshine), Lumina pumpkins, onions, zinnias, cosmos, calendula, Love-in-A-Mist (the red ones this time!), gladiolas, dill, basil, parsley, cilantro, my two potato tubs, a few tomatoes and eggplants, etc. DD1 helped plan the garden with me, and chose yellow beans for both our bush and our pole beans.
This year, I'm growing a lot of beans for drying. I got Peregion, Jacob's Cattle, and a short-season Red Kidney. We are also growing twice as many peas and snow peas. DD2 doesn't like frozen or storebought peas, but will eat them out of the garden. So I'm hoping she'll eat what I freeze from the garden too? Also, the deer got into my peas last year midseason, and both varieties regenerated and looked even better after their pruning. So my Grande Experimente this year is to trim my peas down along one side of my pea fence, and see whether I can generate a good second crop that way.
The girls really like sunflowers - I got our usual sunflower seeds. My aunt suggested that the toxins in their roots had been the reason that my pole beans (planted with them) hadn't done as well last year. I'm thinking about trying that "plant them in a bag of compost" method with them.... ?
We are battling ants, which have for a couple years been removing the compost I add to my strawberry bed, to build themselves a nice anthill. I'm thinking about moving my strawberry bed entirely - they haven't done well there at all, my harvest has been only handfuls. We are in the middle of remodeling the house, with long-term plans to build raised beds and coldframes for the garden, and lots of fruit bushes/trees/perennials to establish. We have four apple trees and a pie cherry already planted (this is year 3 for them), but want to get a raspberry bed, acidify a bed for blueberries, etc. - move to more of our fruit coming from our own yard (we live in town so it's a question of really managing our space well).
My first compost ever. I have restarted my indoor scrap bucket. 
) and we bought a house with a TINY lot in a community with a HOA (vs. the half-acre back home where I could also keep laying hens).
Everything you listed will grow really well in the "cold". I'm not sure about broccoli seeing I've never grown it before but it should be fine. God. What I would do to grow in zone 5!!!!
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