Will a Radeon HD 7850 with an I5 3570K run newer gaming releases at high settings around 60-70 fps?

You're going to want a bigger emphasis on the GPU if you're looking to play newer games

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: AMD FX-6300 3.5GHz 6-Core Processor ($109.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ OutletPC)
Motherboard: Asus M5A97 LE R2.0 ATX AM3+ Motherboard ($76.97 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($58.99 @ NCIX US)
Video Card: Sapphire Radeon R9 280X 3GB Video Card ($299.99 @ Amazon)
Case: Cooler Master Elite 430 ATX Mid Tower Case ($24.99 @ Newegg)
Power Supply: OCZ ZT 650W 80+ Bronze Certified Fully-Modular ATX Power Supply ($59.99 @ Newegg)
Optical Drive: Asus DRW-24F1ST DVD/CD Writer ($15.99 @ Newegg)
Total: $736.88
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-24 18:11 EST-0500)