A Study in Ovarian, Non-Small Cell Lung, Prostate, Colorectal, Gastroesophageal Cancers, and Squamous Cell Carcinoma of the Head and Neck

Inclusion Criteria:

Diagnosis of ovarian, non-small cell lung, prostate, colorectal, gastroesophageal cancer (adenocarcinoma of the esophageal cancer, stomach, or gastroesophageal junction), or squamous cell cancer of the head and neck
Have measurable disease defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 guidelines (except prostate cancer participants)
Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 1
Are willing to follow study procedures for the duration of the study
Are willing to use an approved contraceptive method during treatment and for 3 months after discontinuation of study treatment

Exclusion Criteria:

Have a serious preexisting medical condition that would preclude participation in the study
Are pregnant or lactating
Have received treatment within 28 days of first dose of LY2523355 with a drug that has not received regulatory approval for any indication
Have symptomatic, untreated, or uncontrolled central nervous system (CNS) metastases
Have a second active primary malignancy or a history of a second malignancy requiring cytotoxic therapy
Have QTc interval greater than 470 millisecond (msec) or intraventricular conduction delay (IVCD) with QRS greater than 120 msec on screening electrocardiogram (ECG)
Have active symptomatic fungal, bacterial, and/or known viral infection including active human immunodeficiency virus (HIV) or viral (A, B, C) hepatitis
Participants with pneumonia, evidence of obstructive pneumonitis, other respiratory infections, or infection from other sources are to be excluded