GTX 1070 with AMD Phenom II X4 955 BE + ASUS M4A785TD-V EVO + CM RS-700-PCAA-E3

BF1 is a CPU hog and it is flooring even high end CPU, especially i5s...even 6600k's. While the GTX 1070 would work with your build it would generally be bottlenecked by your CPU. A gtx 1060 6Gb would be a better choice. Also Your PSU is not the best in fact I would replace it as soon as you can with a tier 1 or tier 2 PSU.

I believe we are talking about 1080p right? If so then for this PC max you should go is GTX 1060 or RX 480 for few reasons.
GTX 1070 at 1080p will be utilized like in half when coupled with this CPU. Coupling mid-high grade card with lets face it low-end CPU like this today isn't gonna help you will most of the current games.

And that suggestion above about PSU is a joke. Today those kids can only copy-paste suggestions from other suggestions from other suggestions from a tutorials for dummies. This PSU is far more then fine even with a power hog GPU, for GTX 1070 or anything bellow it's a chill. It might be not the most efficient PSU on earth but it's far from PC killer and certainly better then Corsair CS series being recommended on TH's other topics.
Don't get into this bs... this is words from someone with electronic and IT master degree not a kiddo from his mums basement.

Get the GTX1070 anyway.

-Get a measuring tape and find out how much room you have for a video card. Some of the 3 fan cards are longer.

If you go with a GTX1060 and then upgrade to a i5 or i7 later on or the new RyZen, the GTX1060 will be too slow and you will need to upgrade it so it becomes insane.

The power supply is ok unless it has failing caps or something. The GTX1070 uses less power than the old gpus like the GTX570 did, in fact the HD-5770 is not much less wattage than the GTX1070.

-Consider buying your cpu cooler now instead too. Make sure it will work with your future planned i5 or i7 or other cpu.
With a new massive air cooler you can now overclock that PhenomII for all it's got until you upgrade it.

PCPartPicker part list / Price breakdown by merchant

CPU Cooler: Noctua NH-D15 82.5 CFM CPU Cooler ($81.88 @ OutletPC)
Video Card: EVGA GeForce GTX 1070 8GB SC GAMING Video Card ($384.99 @ NCIX US)
Case: Thermaltake Element G ATX Mid Tower Case
Total: $466.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-30 07:07 EST-0500

I included a case that is maybe close to yours. Do some measuring to be sure first.

A couple of coolers that also looked good. A 3 fan Card if you find out if there is enough room for it.

PCPartPicker part list / Price breakdown by merchant

CPU Cooler: Phanteks PH-TC14PE_BK 78.1 CFM CPU Cooler ($74.99 @ Newegg)
CPU Cooler: CRYORIG R1 Ultimate 76.0 CFM CPU Cooler ($89.89 @ OutletPC)
Video Card: PNY GeForce GTX 1070 8GB XLR8 Video Card ($389.99 @ Newegg)
Case: Thermaltake Element G ATX Mid Tower Case
Total: $554.87
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-12-30 07:29 EST-0500

Your GPU selection is entirely based on what resolution you will be gaming at.

As an example, my system is just a little newer than yours (Socket AM3+ instead of AM3). I started off with a Phenom II (X4 970 or 975, IIRC), then replaced it with the current FX-8320 I'm running a year later. But this was probably 3 years ago, so the monitor we picked isn't quite up to 1080p standards (max resolution is 1600x900, max refresh rate is either 60 or 75Hz, not 100% sure at the moment). I just recently repurposed our old 19" HDTV (max resolution 1366x768) to work as a 2nd monitor, so the chances of my wife agreeing to replacing the monitor with a 1080p or 1440p model are like the old Robert Downey Jr. movie, less than zero. So...if I wanted to upgrade or replace my current GPU (R9 380), there would be little point in me selecting a GTX 1070, let alone a GTX 1080, because they would end up being severely underutilized.

Given the age of your system, I doubt your monitor even hits 1080p resolutions, let alone anything higher. So a GTX 1070 is going to be major overkill for your system. Unless you're going to replace your existing monitor & get a 1440p monitor (or a 1080p/144Hz monitor), I would strongly recommend against spending that much money on a new GPU. If your monitor is like mine & doesn't quite make it to 1080p (i.e. max resolution is something like 1280x960, 1440x900/960, or 1600x900), you'll probably be more than OK with a GTX 1050Ti instead, but you might want to consider the GTX 1060 (or even an RX 470/480) for future monitors.

As a side note, there's not a whole lot you can do in the CPU department. The 2 best choices (Phenom II X4 980 or X6 1100T) are only maybe a step better than your current CPU (http://www.tomshardware.com/reviews/cpu-hierarchy,4312.html), & are still going to struggle with games like BF1. Which is another reason to save some money on your GPU, so that you can start saving up for a new motherboard/CPU/RAM set. For that, I would recommend waiting a bit until Ryzen comes out from AMD, so that when it's been benchmarked we have a better idea of how it stacks up against Intel's offerings.

@ Up. Applause mate. Op is gonna get a brain meltdown coz of all those decisions right now but at least he is now well informed lol

Let's complicate things even more. If you are thinking long term then first of all pick resolution and refresh rate you are aiming for your next display. This will vasty determine your next choice. Also while looking at your future display take a Freesync/Gsync into consideration. This might be a best next step in your gaming experience, but will also determine which side Nvidia or AMD you will have to choose to get a full advantage.
For this moment if you aim for 1080p at above 60 fps and very high quality then RX 480/GTX 1060 will be enough.
But if you aim at 1440p above 60fps then even GTX1070 might not be enough to cover all the games, on the AMD side ..... waiting for the Vega since RX 480 is IMHO not enough, hence that's also why I'm still hammering my 10 years old 24" 1080p panel. I want 27"/1440p/144Hz Freesync display but there is noting to power it up.
So think what in future will satisfy your needs and keep building PC until you are there.