SPI on STM32F407 Discovery not working

I am trying to program an F407VG manually without using CubeMX and using registers. Could someone please help me get the SPI running? When I look on an oscilloscope, the Slave/Chip select goes low and high correctly but I am writing data to SPI1 DR and I don't see anything on MOSI or SCLK. What have I done wrong? C code below:

/* ENABLING AND CONFIGURING CLOCKS */
RCC->AHB1ENR |= (1<<0); //GPIO config
RCC->AHB1ENR |= (1<<4);
RCC->APB2ENR |= (1<<12); // SPI_1 Enabled
RCC->CR |= (1<<0); // Enable the 16 MHz HSI clock
RCC->PLLCFGR |= (0<<22); // Set HSI as source
RCC->PLLCFGR |= (1<<1) | (0<<0); // Adjust to use PLL

// Set the divider PLL_M to 16 to get 1 MHz since HSI is 16 MHz
RCC->PLLCFGR |= (0<<0) | (0<<1) | (0<<2) | (0<<3) | (1<<4) | (0<<5);

// SET PLL_N as 288
RCC->PLLCFGR |= (0<<6) | (0<<7) | (0<<8) | (0<<9) | (0<<10) | (1<<11) | (0<<12) | (0<<13) | (1<<14);

// Set PLL_P as 4 to get 72 MHz
RCC->PLLCFGR |= (1<<16) | (0<<17);

// Set APB2 divider to 2 to get 36 MHz
RCC->PLLCFGR |= (1<<15) | (0<<14) | (0<<13);

/*GPIO PINS*/
//Set PE5 as output for CS, push pull, no pull up/down
GPIOE->MODER |= (1<<10);
GPIOE->OTYPER |= (0<<5);
GPIOE->OSPEEDR |= (1<<10);
GPIOE->PUPDR |= (00<<10);
GPIOE->BSRR |= (1<<5);

// Set PA5 as SCLK using AF5
GPIOA->MODER |= (1<<11);
GPIOA->OTYPER |= (0<<5);
GPIOA->OSPEEDR |= (1<<10);
GPIOA->PUPDR |= (1<<10);
GPIOA->AFR[0] |= (1<<22) | (1<<20);

// Set PA6 as MISO using AF5
GPIOA->MODER |= (1<<13); 
GPIOA->OTYPER |= (0<<6);
GPIOA->OSPEEDR |= (1<<13);
GPIOA->PUPDR |= (1<<12);
GPIOA->AFR[0] |= (1<<24) | (1<<26);

// Set PA7 as MOSI using AF5
GPIOA->MODER |= (1<<15);
GPIOA->OTYPER |= (0<<7);
GPIOA->OSPEEDR |= (1<<15);
GPIOA->PUPDR |= (1<<14);
GPIOA->AFR[0] |= (1<<28) | (1<<30);

/* Configure SPI */
/* SPI is set as
Master Mode
Direction 2 Lines
8-Bit data size
Clock polarity low
Clock phase 1 Edge
Baudrate prescalre of 32
Send the MSB first
CRC disabled
Software set NSS/CS
*/
SPI1->CR1 |= (0<<15) | (1<<14) | (0<<13) | (0<<11) | ...
(0<<10) | (1<<9) | (0<<7) | (1<<6) | (1<<5) | (0<<4) | ...
(0<<3) | (1<<2) | (0<<1) | (0<<0);

When running the code I set the CS pin to low and then write random data to the SPI1 DR like this:

GPIOE->BSRR |= (0<<5);
Delay by 10000
SPI1->DR |= (1<<7) | (1<<2);

Delay by 50
SPI1->DR |= (0<<7) | (0<<2);
Delay by 10000
GPIOE->BSRR |= (1<<5);


The delay is just a simple counter function. So in summary, I am configuring the HSI to be a source for PLL and then setting the division and multiplication factors such that the output frequency to APB/AHB is 72MHz. SPI1 is on APB2 so after dividing 72MHz by a prescaler of 2, I get 36 MHz as the clock frequency for SPI1 since I have read that SPI1 should be around 36 MHz. I have been through the code and registers again but I cannot find my error. Thank you for your help.